{"id":31697,"date":"2022-01-13T22:04:48","date_gmt":"2022-01-13T14:04:48","guid":{"rendered":"https:\/\/swarma.org\/?p=31697"},"modified":"2022-01-13T22:04:48","modified_gmt":"2022-01-13T14:04:48","slug":"%e9%80%9a%e5%be%80%e5%ad%aa%e7%94%9f%e8%b4%a8%e6%95%b0%e7%8c%9c%e6%83%b3%e7%9a%84%e5%9e%ab%e8%84%9a%e7%9f%b3%ef%bc%9a%e5%9b%be%e8%ae%ba%e5%b8%ae%e5%8a%a9%e6%95%b0%e5%ad%a6%e5%ae%b6%e7%a0%b4%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=31697","title":{"rendered":"\u901a\u5f80\u5b6a\u751f\u8d28\u6570\u731c\u60f3\u7684\u57ab\u811a\u77f3\uff1a\u56fe\u8bba\u5e2e\u52a9\u6570\u5b66\u5bb6\u7834\u89e3\u8d28\u6570\u7684\u9634\u8c0b"},"content":{"rendered":"
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\u7814\u7a76\u9886\u57df\uff1a<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong>\u56fe\u8bba\uff0c\u6570\u8bba\uff0c\u968f\u673a\u6e38\u8d70<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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Jordana Cepelewicz<\/span> <\/span>| \u4f5c\u8005<\/strong><\/span><\/p>\n

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\u5f90\u6069\u5ce4<\/span> <\/span>| \u8bd1\u8005<\/strong><\/span><\/strong><\/span><\/p>\n

\u6881\u91d1<\/span> | \u5ba1\u6821<\/strong><\/span><\/strong><\/span><\/p>\n

\u9093\u4e00\u96ea<\/span> | \u7f16\u8f91<\/strong><\/span><\/p>\n<\/section>\n


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\u4e00\u9879\u65b0\u7684\u8bc1\u660e\u63ed\u7a7f\u4e86\u4e00\u4e2a\u9634\u8c0b\uff0c\u6570\u5b66\u5bb6\u66fe\u62c5\u5fc3\u5b83\u4f1a\u50cf\u4e4c\u4e91\u4e00\u6837\u76d8\u65cb\u5728\u6570\u8f74\u4e4b\u4e0a\u3002\u800c\u5728\u8bc1\u660e\u8fc7\u7a0b\u4e2d\uff0c\u6570\u5b66\u5bb6\u4eec\u5f00\u53d1\u4e86\u53e6\u4e00\u5957\u5de5\u5177\u6765\u7406\u89e3\u7b97\u672f\u7684\u57fa\u672c\u7ec4\u6210\u90e8\u5206\u2014\u2014\u8d28\u6570\u3002<\/span><\/p>\n


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\u57282021\u5e743\u6708\u53d1\u8868\u7684\u4e00\u7bc7\u8bba\u6587\u4e2d\uff0c\u5fb7\u56fd\u54e5\u5ef7\u6839\u5927\u5b66\u7684 Harald Helfgott \u548c\u52a0\u5dde\u7406\u5de5\u5b66\u9662\u7684 Maksym Radziwi\u0142\u0142 \u63d0\u51fa\u4e86\u4e00\u4e2a\u6539\u8fdb\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u4ee5\u89e3\u51b3\u4e54\u62c9\u731c\u60f3<\/strong><\/span>\uff08Chowla conjecture\uff09<\/span>\u7684\u7279\u5b9a\u8868\u8ff0\u2014\u2014\u8fd9\u662f\u4e00\u4e2a\u5173\u4e8e\u6574\u6570\u4e4b\u95f4\u5173\u7cfb\u7684\u95ee\u9898\u3002\u8be5\u731c\u60f3\u9884\u6d4b\uff0c\u4e00\u4e2a\u6574\u6570\u662f\u6709\u5947\u6570\u8fd8\u662f\u5076\u6570\u4e2a\u8d28\u56e0\u6570\uff0c\u5e76\u4e0d\u5f71\u54cd\u5b83\u524d\u540e\u7684\u6574\u6570\u662f\u6709\u5947\u6570\u8fd8\u662f\u5076\u6570\u4e2a\u8d28\u56e0\u6570\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u76f8\u90bb\u6574\u6570\u7684\u67d0\u4e9b\u6700\u57fa\u672c\u7684\u7b97\u672f\u5c5e\u6027\u4e0d\u4f1a\u6709\u7279\u5b9a\u65b9\u5f0f\u7684\u5173\u8054\u3002<\/span><\/p>\n


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\u8fd9\u4e2a\u770b\u4f3c\u7b80\u5355\u7684\u60f3\u6cd5\u4e0e\u6570\u5b66\u4e2d\u4e00\u4e9b\u5173\u4e8e\u8d28\u6570\u7684\u6700\u6df1\u523b\u95ee\u9898\u4ea4\u7ec7\u5728\u4e00\u8d77\u3002\u52a0\u5dde\u5927\u5b66\u6d1b\u6749\u77f6\u5206\u6821\u7684\u9676\u54f2\u8f69<\/span>\uff08Terence Tao\uff09<\/span>\u8bf4\uff0c\u8bc1\u660e\u4e54\u62c9\u731c\u60f3\u662f\u56de\u7b54\u8fd9\u4e9b\u66f4\u68d8\u624b\u95ee\u9898\u7684\u201c\u70ed\u8eab\u6216\u8005\u8bf4\u57ab\u811a\u77f3\u201d\u3002<\/span><\/p>\n


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\u7136\u800c\u51e0\u5341\u5e74\u6765\uff0c\u8fd9\u6837\u7684\u70ed\u8eab\u95ee\u9898\u672c\u8eab\u5c31\u6210\u4e86\u4e00\u9879\u51e0\u4e4e\u4e0d\u53ef\u80fd\u5b8c\u6210\u7684\u4efb\u52a1\u3002\u6570\u5b66\u5bb6\u4eec\u4e5f\u662f\u5728\u77ed\u77ed\u51e0\u5e74\u4ee5\u524d\u624d\u53d6\u5f97\u4e86\u4e00\u4e9b\u5c0f\u5c0f\u8fdb\u5c55\uff0c\u5f53\u65f6\u9676\u54f2\u8f69\u8bc1\u660e\u4e86\u8fd9\u4e2a\u95ee\u9898\u7684\u4e00\u4e2a\u66f4\u7b80\u5355\u7684\u7248\u672c\uff0c\u79f0\u4e3a\u5bf9\u6570\u4e54\u62c9\u731c\u60f3<\/strong><\/span>\uff08logarithmic Chowla conjecture\uff09<\/span>\u3002\u867d\u7136\u4ed6\u4f7f\u7528\u7684\u6280\u672f\u88ab\u8ba4\u4e3a\u5bcc\u6709\u521b\u65b0\u6027\u4e14\u4ee4\u4eba\u5174\u594b\uff0c\u4f46\u5f97\u5230\u7684\u7ed3\u679c\u4e0d\u591f\u7cbe\u786e\uff0c\u65e0\u6cd5\u5e2e\u52a9\u5728\u76f8\u5173\u95ee\u9898\u4e0a\u53d6\u5f97\u66f4\u591a\u8fdb\u5c55\uff0c\u5305\u62ec\u5173\u4e8e\u8d28\u6570\u7684\u95ee\u9898\u3002\u6570\u5b66\u5bb6\u5e0c\u671b\u8fd8\u80fd\u6709\u4e00\u4e2a\u66f4\u5f3a\u5927\u3001\u66f4\u666e\u9002\u7684\u8bc1\u660e\u3002<\/span><\/p>\n


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\u56fe1. \u9676\u54f2\u8f69\u5f00\u53d1\u4e86\u4e00\u79cd\u7b56\u7565\uff0c\u4f7f\u7528\u6269\u5c55\u56fe\uff08expander graph\uff09\u6765\u56de\u7b54\u4e54\u62c9\u731c\u60f3\u7684\u5bf9\u6570\u7248\u672c\uff0c\u4f46\u8be5\u7b56\u7565\u76ee\u524d\u65e0\u6cd5\u5b8c\u5168\u53d1\u6325\u4f5c\u7528\u3002| \u6765\u6e90\uff1a\u52a0\u5dde\u5927\u5b66\u6d1b\u6749\u77f6\u5206\u6821<\/span><\/section>\n


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\u73b0\u5728\uff0cHelfgott \u548c Radziwi\u0142\u0142 \u63d0\u4f9b\u4e86\u8fd9\u6837\u4e00\u4e2a\u8bc1\u660e\u3002\u4ed6\u4eec\u7684\u89e3\u51b3\u65b9\u6848\u5c06\u56fe\u8bba<\/span>\uff08graph theory\uff09<\/span>\u6280\u672f\u76f4\u63a5\u63a8\u5411\u6570\u8bba<\/span>\uff08number theory\uff09<\/span>\u7684\u6838\u5fc3\uff0c\u91cd\u65b0\u70b9\u71c3\u4e86\u4e54\u62c9\u731c\u60f3\u5151\u73b0\u5176\u627f\u8bfa\u7684\u5e0c\u671b\u2014\u2014\u4e3a\u6570\u5b66\u5bb6\u63d0\u4f9b\u6700\u7ec8\u5f15\u5bfc\u4ed6\u4eec\u89e3\u51b3\u4e00\u4e9b\u6700\u96be\u4ee5\u6349\u6478\u95ee\u9898\u6240\u9700\u8981\u7684\u60f3\u6cd5\u3002<\/span><\/p>\n


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\u8d28\u6570\u672c\u8eab\u662f\u7528\u4e58\u6cd5\u5b9a\u4e49\u7684\uff1a\u5b83\u4eec\u4e0d\u80fd\u88ab\u9664\u81ea\u8eab\u548c 1 \u4ee5\u5916\u7684\u4efb\u4f55\u6570\u5b57\u6574\u9664\uff1b\u5b83\u4eec\u76f8\u4e58\u5219\u4f1a\u6784\u6210\u5176\u4f59\u7684\u6574\u6570\u3002\u4f46\u662f\u51e0\u4e2a\u4e16\u7eaa\u4ee5\u6765\uff0c\u6d89\u53ca\u52a0\u6cd5\u7684\u8d28\u6570\u95ee\u9898\u4e00\u76f4\u56f0\u6270\u7740\u6570\u5b66\u5bb6\u3002\u4f8b\u5982\uff0c\u5b6a\u751f\u8d28\u6570\u731c\u60f3\u65ad\u8a00\u6709\u65e0\u7a77\u591a\u4e2a\u76f8\u5dee 2 \u7684\u8d28\u6570<\/span>\uff08\u5982 11 \u548c 13\uff09<\/span>\u3002\u8fd9\u4e2a\u95ee\u9898\u8fde\u63a5\u4e86\u4e58\u6cd5\u548c\u52a0\u6cd5\u4e24\u4e2a\u901a\u5e38\u76f8\u4e92\u72ec\u7acb\u7684\u7b97\u672f\u8fd0\u7b97\uff0c\u56e0\u800c\u5177\u6709\u6311\u6218\u6027\u3002<\/strong>\u201c\u8fd9\u5f88\u56f0\u96be\uff0c\u56e0\u4e3a\u6211\u4eec\u6df7\u5408\u4e86\u4e24\u4e2a\u4e16\u754c\uff0c\u201d\u5e03\u91cc\u65af\u6258\u5927\u5b66\u7684 Oleksiy Klurman \u8bf4\u3002<\/span><\/p>\n


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\u76f4\u89c9\u544a\u8bc9\u6570\u5b66\u5bb6\uff0c\u4e00\u4e2a\u6570\u52a0 2 \u5e94\u8be5\u5b8c\u5168\u6539\u53d8\u5b83\u7684\u4e58\u6cd5\u7ed3\u6784\u2014\u2014\u8fd9\u610f\u5473\u7740\u4e00\u4e2a\u6570\u662f\u5426\u662f\u8d28\u6570<\/span>\uff08\u4e00\u79cd\u4e58\u6cd5\u6027\u8d28\uff09<\/span>\u548c\u4e24\u4e2a\u5355\u4f4d\u4e4b\u5916\u7684\u6570\u662f\u5426\u662f\u8d28\u6570<\/span>\uff08\u4e00\u79cd\u52a0\u6cd5\u6027\u8d28\uff09<\/span>\u4e4b\u95f4\u5e94\u8be5\u6ca1\u6709\u76f8\u5173\u6027\u3002\u6570\u8bba\u5bb6\u6ca1\u6709\u53d1\u73b0\u4efb\u4f55\u8bc1\u636e\u8868\u660e\u5b58\u5728\u8fd9\u79cd\u76f8\u5173\u6027\uff0c\u4f46\u5982\u679c\u6ca1\u6709\u8bc1\u660e\uff0c\u4ed6\u4eec\u4e5f\u4e0d\u80fd\u6392\u9664\u76f8\u5173\u6027\u51fa\u73b0\u7684\u53ef\u80fd\u6027\u3002<\/span><\/p>\n


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\u6ca1\u6709\u4eba\u63a5\u8fd1\u6392\u9664\u8fd9\u6837\u7684\u9634\u8c0b\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u5728 1965 \u5e74\uff0c\u4e54\u62c9<\/span>\uff08Sarvadaman Chowla\uff09<\/span>\u5236\u5b9a\u4e86\u4e00\u79cd\u7a0d\u5fae\u7b80\u5355\u7684\u65b9\u6cd5\u6765\u601d\u8003\u90bb\u8fd1\u6570\u5b57\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u4ed6\u60f3\u8bc1\u660e\uff0c\u4e00\u4e2a\u6574\u6570\u662f\u5177\u6709\u5076\u6570\u6216\u5947\u6570\u4e2a\u7684\u8d28\u56e0\u6570<\/strong>\u2014\u2014\u8fd9\u4e00\u6761\u4ef6\u88ab\u79f0\u4e3a\u5176\u8d28\u6570\u6570\u91cf\u7684\u201c\u5947\u5076\u6027\u201d<\/span>\uff08parity\uff09<\/span>\u2014\u2014\u4e0d\u5e94\u8be5\u4ee5\u4efb\u4f55\u65b9\u5f0f\u5f71\u54cd\u5176\u76f8\u90bb\u6574\u6570\u8d28\u56e0\u6570\u7684\u6570\u91cf<\/strong>\u3002<\/span><\/p>\n


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\u8fd9\u4e2a\u9648\u8ff0\u901a\u5e38\u7528\u5218\u7ef4\u5c14\u51fd\u6570<\/span>\uff08Liouville function\uff09<\/span>\u6765\u7406\u89e3\uff0c\u5982\u679c\u6574\u6570\u6709\u5947\u6570\u4e2a\u8d28\u56e0\u6570<\/span>\uff08\u5982 12 = 2 \u00d7 2 \u00d7 3\uff09<\/span>\uff0c\u5219\u5b83\u4e3a\u6574\u6570\u8d4b\u503c -1\uff1b\u5982\u679c\u6574\u6570\u6709\u5076\u6570\u4e2a\u8d28\u56e0\u6570<\/span>\uff08\u5982 10 = 2 \u00d7 5\uff09<\/span>\uff0c\u5219\u5b83\u4e3a\u6574\u6570\u8d4b\u503c +1\u3002\u4e54\u62c9\u731c\u60f3\u9884\u6d4b\uff0c\u5218\u7ef4\u5c14\u51fd\u6570\u7684\u76f8\u90bb\u53d6\u503c\u4e4b\u95f4\u5e94\u8be5\u6ca1\u6709\u76f8\u5173\u6027\u3002<\/strong><\/span><\/p>\n


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<\/section>\n
\u56fe2. \u524d10\u4e2a\u6574\u6570\u7684\u5218\u7ef4\u5c14\u503c\uff0c\u53ca\u5176\u8d28\u56e0\u6570\u5206\u89e3\u7684\u79bb\u6563\u56fe\u3002\u4f8b\u5982 6 = 2×3\uff0c\u6709\u5076\u6570\u4e2a\u8d28\u56e0\u6570\uff0c\u5218\u7ef4\u5c14\u503c\u4e3a +1\uff0c8 = 2x2x2\uff0c\u6709\u5947\u6570\u4e2a\u8d28\u56e0\u6570\uff0c\u5218\u7ef4\u5c14\u503c\u4e3a-1\u3002| \u6765\u6e90\uff1a\u8bd1\u8005\u7ed8\u5236 [1]<\/span><\/section>\n


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\u5728\u63a2\u7a76\u5947\u5076\u6027\u65f6\uff0c\u8bb8\u591a\u7814\u7a76\u8d28\u6570\u7684\u6700\u5148\u8fdb\u65b9\u6cd5\u90fd\u5931\u8d25\u4e86\uff0c\u800c\u4e54\u62c9\u731c\u60f3\u6b63\u662f\u8981\u7814\u7a76\u5947\u5076\u6027\u95ee\u9898\u3002\u6570\u5b66\u5bb6\u5e0c\u671b\u901a\u8fc7\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u53ef\u4ee5\u53d1\u5c55\u51fa\u65b0\u60f3\u6cd5\u5e94\u7528\u4e8e\u8bf8\u5982\u5b6a\u751f\u8d28\u6570\u731c\u60f3\u7b49\u95ee\u9898\u3002\u7136\u800c\uff0c\u591a\u5e74\u6765\uff0c\u5b83\u4ecd\u7136\u53ea\u662f\u4e00\u4e2a\u5e7b\u60f3\u4e2d\u7684\u5e0c\u671b\u3002\u4e0d\u8fc7\uff0c\u5728 2015 \u5e74\uff0c\u4e00\u5207\u5f00\u59cb\u6539\u53d8\u3002<\/span><\/p>\n


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2. \u610f\u5916\u7a81\u7834\uff1a\u5947\u5076\u7c07\u70df\u6d88\u4e91\u6563<\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


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\u82ac\u5170\u56fe\u5c14\u5e93\u5927\u5b66\u7684 Radziwi\u0142\u0142 \u548c Kaisa Matom\u00e4ki \u5e76\u6ca1\u6709\u7740\u624b\u89e3\u51b3\u4e54\u62c9\u731c\u60f3\u3002\u76f8\u53cd\uff0c\u4ed6\u4eec\u60f3\u7814\u7a76\u5218\u7ef4\u5c14\u51fd\u6570\u5728\u4e00\u6bb5\u77ed\u533a\u95f4\u4e0a\u7684\u884c\u4e3a\u3002\u4ed6\u4eec\u5df2\u7ecf\u77e5\u9053\uff0c\u8be5\u51fd\u6570\u7684\u53d6\u503c\u5728\u6574\u4e2a\u6b63\u6574\u6570\u57df\u4e0a\u5e73\u5747\u6765\u770b\u4e3a +1\uff0c -1\u5404\u534a\uff1b\u4f46\u5b83\u7684\u503c\u4ecd\u7136\u6709\u53ef\u80fd\u805a\u96c6\u5728\u4e00\u8d77\uff0c\u5728\u67d0\u4e2a\u8f83\u957f\u7684\u8fde\u7eed\u533a\u95f4\u5185\u7684\u53d6\u503c\u8981\u4e48\u5168\u90e8\u4e3a +1\uff0c\u8981\u4e48\u5168\u90e8\u4e3a -1\uff0c\u4ece\u800c\u5f62\u6210\u56e2\u7c07\u3002<\/span><\/p>\n


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\u56fe3. \u4e3a1\u81f3n\u4e4b\u95f4\u7684\u6574\u6570\u7edf\u8ba1\u5218\u7ef4\u5c14\u503c\u7684\u5e73\u5747\u503c\uff0cn \u622a\u6b62\u81f310000\u7684\u5bf9\u6570\u7ebf\u6027\u56fe\u3002\u968f\u7740n\u589e\u5927\uff0c\u7edf\u8ba1\u503c\u9010\u6e10\u903c\u8fd10\uff0c\u8868\u660e\u51fd\u6570\u53d6\u503c\u8d8b\u8fd1 +1\uff0c -1 \u5404\u534a\u3002| \u6765\u6e90\uff1a\u8bd1\u8005\u7ed8\u5236 [1]<\/span><\/section>\n


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2015 \u5e74\uff0cMatom\u00e4ki \u548c Radziwi\u0142\u0142 \u8bc1\u660e\u8fd9\u4e9b\u56e2\u7c07\u51e0\u4e4e\u4ece\u4e0d\u51fa\u73b0\u3002\u4ed6\u4eec\u4e8e\u6b21\u5e74\u53d1\u8868\u7684\u7814\u7a76\u8868\u660e\uff0c\u5982\u679c\u9009\u62e9\u4e00\u4e2a\u968f\u673a\u6570\u5e76\u67e5\u770b\u5b83\u7684\u6210\u767e\u4e0a\u5343\u4e2a\u6700\u8fd1\u90bb\uff0c\u5927\u7ea6\u4e00\u534a\u6574\u6570\u7684\u8d28\u56e0\u6570\u6570\u91cf\u662f\u5076\u6570\uff0c\u53e6\u4e00\u534a\u662f\u5947\u6570\u3002<\/strong><\/span><\/p>\n


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<\/section>\n
\u56fe4. \u4e3a1\u81f3n\u4e4b\u95f4\u7684\u6574\u6570\u6309\u5176\u5218\u7ef4\u5c14\u503c\u5206\u7ec4\uff0c\u7edf\u8ba1\u4e0b\u4e00\u4e2a\u6570\u7684\u5218\u7ef4\u5c14\u503c\u5e73\u5747\u503c\uff0cn \u622a\u6b62\u81f310000\u7684\u5bf9\u6570\u7ebf\u6027\u56fe\u3002\u4e0d\u8bba\u662f\u54ea\u4e00\u7ec4\uff0c\u7edf\u8ba1\u503c\u90fd\u5728\u903c\u8fd10\uff0c\u8fd9\u53ef\u4ee5\u63d0\u4f9b\u5173\u4e8e\u4e54\u62c9\u731c\u60f3\u7684\u76f4\u89c9\u3002| \u6765\u6e90\uff1a\u8bd1\u8005\u7ed8\u5236 [1]<\/span><\/section>\n


<\/p>\n

\u201c\u8fd9\u662f\u62fc\u56fe\u4e2d\u7f3a\u5c11\u7684\u91cd\u8981\u90e8\u5206\uff0c\u201d\u8499\u7279\u5229\u5c14\u5927\u5b66\u7684 Andrew Granville \u8bf4\u3002\u201c\u4ed6\u4eec\u53d6\u5f97\u4e86\u4ee4\u4eba\u96be\u4ee5\u7f6e\u4fe1\u7684\u7a81\u7834\uff0c\u5f7b\u5e95\u6539\u53d8\u4e86\u6574\u4e2a\u4e3b\u9898\u3002\u201d<\/span><\/p>\n


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\u8fd9\u662f\u4e00\u4e2a\u5f3a\u6709\u529b\u7684\u8bc1\u636e\uff0c\u63d0\u793a\u6570\u5b57\u5e76\u4e0d\u662f\u4e0a\u8ff0\u5927\u89c4\u6a21\u9634\u8c0b\u7684\u540c\u8c0b\u2014\u2014\u4e0d\u8fc7\uff0c\u4e54\u62c9\u731c\u60f3\u662f\u5ef6\u4f38\u5230\u6574\u4e2a\u6570\u8f74\u7684\u6700\u9ad8\u7ea7\u522b\u7684\u9634\u8c0b\u3002\u8fd9\u5c31\u662f\u9676\u54f2\u8f69\u8fdb\u5165\u7684\u5730\u65b9\u3002\u51e0\u4e2a\u6708\u540e\uff0c\u4ed6\u53d1\u73b0\u4e00\u79cd\u65b9\u6cd5\u53ef\u4ee5\u5728 Matom\u00e4ki \u548c Radziwi\u0142\u0142 \u5de5\u4f5c\u7684\u57fa\u7840\u4e0a\u89e3\u51b3\u4e00\u4e2a\u66f4\u5bb9\u6613\u7814\u7a76\u7684\u95ee\u9898\uff0c\u5373\u5bf9\u6570\u4e54\u62c9\u731c\u60f3\u3002\u5728\u8fd9\u4e2a\u516c\u5f0f\u4e2d\uff0c\u8f83\u5c0f\u7684\u6570\u5b57\u88ab\u8d4b\u4e88\u8f83\u5927\u7684\u6743\u91cd\uff0c\u4ee5\u4fbf\u4e0e\u8f83\u5927\u7684\u6574\u6570\u4e00\u6837\u88ab\u91c7\u6837\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u9676\u54f2\u8f69\u8bd5\u56fe\u7528\u53cd\u8bc1\u6cd5\u8bc1\u660e\u5bf9\u6570\u4e54\u62c9\u731c\u60f3\u3002\u9996\u5148\uff0c\u4ed6\u5047\u8bbe\u5bf9\u6570\u4e54\u62c9\u731c\u60f3\u662f\u9519\u8bef\u7684\u2014\u2014\u4e8b\u5b9e\u4e0a\uff0c\u8fde\u7eed\u6574\u6570\u7684\u8d28\u56e0\u6570\u6570\u91cf\u4e4b\u95f4\u5b58\u5728\u4e00\u4e2a\u9634\u8c0b\u3002\u7136\u540e\u4ed6\u8bd5\u56fe\u8bc1\u660e\u8fd9\u6837\u7684\u9634\u8c0b\u53ef\u4ee5\u88ab\u653e\u5927\uff1a\u4e54\u62c9\u731c\u60f3\u7684\u4e00\u4e2a\u4f8b\u5916\u4e0d\u4ec5\u610f\u5473\u7740\u8fde\u7eed\u6574\u6570\u4e4b\u95f4\u7684\u9634\u8c0b\uff0c\u800c\u4e14\u610f\u5473\u7740\u6cbf\u7740\u6574\u4e2a\u6570\u8f74\u7684\u66f4\u5927\u9634\u8c0b\u3002\u7136\u540e\uff0c\u4ed6\u5c31\u80fd\u591f\u5229\u7528 Radziwi\u0142\u0142 \u548c Matom\u00e4ki \u65e9\u5148\u7684\u7ed3\u679c\uff0c\u5b83\u6070\u597d\u6392\u9664\u4e86\u8fd9\u79cd\u66f4\u5927\u7684\u9634\u8c0b\u3002\u4e54\u62c9\u731c\u60f3\u7684\u53cd\u4f8b\u4f1a\u5bfc\u81f4\u903b\u8f91\u4e0a\u7684\u77db\u76fe\u2014\u2014\u4ece\u800c\u8bc1\u660e\u53cd\u4f8b\u4e0d\u53ef\u80fd\u5b58\u5728\uff0c\u731c\u60f3\u5fc5\u987b\u4e3a\u771f\u3002<\/span><\/p>\n


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\u4f46\u5728\u9676\u54f2\u8f69\u80fd\u505a\u4e0a\u8ff0\u4efb\u4f55\u63a8\u7406\u4e4b\u524d\uff0c\u4ed6\u5fc5\u987b\u60f3\u51fa\u4e00\u79cd\u8fde\u63a5\u6570\u5b57\u7684\u65b0\u65b9\u6cd5\u3002<\/span><\/p>\n


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3. \u56fe\u2014\u2014\u8fde\u63a5\u6570\u5b57<\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u9676\u54f2\u8f69\u9996\u5148\u5229\u7528\u4e86\u5218\u7ef4\u5c14\u51fd\u6570\u7684\u4e00\u4e2a\u5b9a\u4e49\u7279\u5f81\u3002\u8003\u8651\u6570\u5b57 2 \u548c 3\uff0c\u4e24\u8005\u90fd\u6709\u5947\u6570\u4e2a\u8d28\u56e0\u6570\uff0c\u56e0\u6b64\u5218\u7ef4\u5c14\u503c\u90fd\u4e3a -1\u3002\u4f46\u56e0\u4e3a\u5218\u7ef4\u5c14\u51fd\u6570\u662f\u4e58\u6cd5\u7684\uff0c\u6240\u4ee5 2 \u548c 3 \u7684\u500d\u6570\u4e5f\u6709\u76f8\u540c\u7684\u7b26\u53f7\u6a21\u5f0f\u3002<\/span><\/p>\n


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\u8fd9\u4e2a\u7b80\u5355\u7684\u4e8b\u5b9e\u5177\u6709\u91cd\u8981\u7684\u542b\u4e49\u3002\u5982\u679c2 \u548c 3 \u90fd\u6709\u5947\u6570\u4e2a\u8d28\u56e0\u6570\u662f\u7531\u4e8e\u67d0\u79cd\u79d8\u5bc6\u9634\u8c0b\uff0c\u90a3\u4e48 4 \u548c 6 \u4e4b\u95f4\u4e5f\u5b58\u5728\u9634\u8c0b\u2014\u2014\u6570\u5b57\u76f8\u5dee\u4e0d\u662f 1\uff0c\u800c\u662f\u76f8\u5dee 2\u3002\u7531\u6b64\u5f00\u59cb\u4e8b\u60c5\u53d8\u5f97\u66f4\u7cdf\uff1a\u76f8\u90bb\u6574\u6570\u4e4b\u95f4\u7684\u9634\u8c0b\u4e5f\u610f\u5473\u7740\u5176\u6240\u6709\u500d\u6570\u5bf9\u4e4b\u95f4\u7684\u9634\u8c0b\u3002\u201c\u5bf9\u4e8e\u4efb\u4f55\u8d28\u6570\uff0c\u8fd9\u4e9b\u9634\u8c0b\u90fd\u4f1a\u968f\u500d\u6570\u653e\u5927\u800c\u4f20\u64ad\u5f00\u6765\u3002\u201d\u9676\u54f2\u8f69\u8bf4\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u4e3a\u4e86\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e2a\u4e0d\u65ad\u6269\u5927\u7684\u9634\u8c0b\uff0c\u9676\u54f2\u8f69\u4ece\u56fe\u7684\u89d2\u5ea6\u6765\u601d\u8003\u5b83\uff0c\u56fe\u662f\u7531\u8fb9<\/span>\u8fde\u63a5\u7684\u9876\u70b9<\/span>\u7684\u96c6\u5408\u3002\u5728\u8fd9\u4e2a\u6570\u5b57\u56fe\u4e2d\uff0c\u6bcf\u4e2a\u9876\u70b9\u4ee3\u8868\u4e00\u4e2a\u6574\u6570\u3002\u5982\u679c\u4e24\u4e2a\u6570\u76f8\u5dee\u4e00\u4e2a\u8d28\u6570\u5e76\u4e14\u4e5f\u80fd\u88ab\u8be5\u8d28\u6570\u6574\u9664\uff0c\u5219\u5b83\u4eec\u7531\u4e00\u6761\u8fb9\u8fde\u63a5\u3002<\/strong><\/span><\/p>\n


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\u4f8b\u5982\uff0c\u8003\u8651\u6570\u5b57 1001\uff0c\u5b83\u53ef\u4ee5\u88ab\u8d28\u6570 7\u300111 \u548c 13 \u6574\u9664\u3002\u5728\u9676\u54f2\u8f69\u7684\u56fe\u4e2d\uff0c\u5b83\u4e0e 1008\u30011012 \u548c 1014<\/span>\uff08\u901a\u8fc7\u4e00\u6b21\u52a0\u6cd5\uff09<\/span>\u4ee5\u53ca 994\u3001990 \u548c 988<\/span>\uff08\u901a\u8fc7\u4e00\u6b21\u51cf\u6cd5\uff09<\/span>\u5171\u4eab\u8fb9\u3002\u8fd9\u4e9b\u6570\u5b57\u4e2d\u7684\u6bcf\u4e00\u4e2a\u4f9d\u6b21\u8fde\u63a5\u5230\u8bb8\u591a\u5176\u4ed6\u9876\u70b9\u3002<\/span><\/p>\n


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<\/p>\n

\u56fe5. \u5728\u9676\u54f2\u8f69\u7684\u56fe\u4e2d\uff0c\u6bcf\u4e2a\u9876\u70b9\u4ee3\u8868\u4e00\u4e2a\u6574\u6570\u3002\u5982\u679c\u4e24\u4e2a\u6570\u76f8\u5dee\u4e00\u4e2a\u8d28\u6570\u5e76\u4e14\u4e5f\u80fd\u88ab\u8be5\u8d28\u6570\u6574\u9664\uff0c\u5219\u5b83\u4eec\u7531\u4e00\u6761\u8fb9\u8fde\u63a5\u3002<\/span>
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\u56fe6. Harald Helfgott \u548c Maksym Radziwi\u0142\u0142 \u8bbe\u8ba1\u4e86\u4e00\u79cd\u7b80\u5355\u7684\u56fe\u6765\u7814\u7a76\u6574\u6570\u3002\u6574\u6570\u4e4b\u95f4\u53ea\u8981\u76f8\u5dee\u4e00\u4e2a\u8d28\u6570\u5c31\u4f1a\u8fde\u63a5\u3002\u4ed6\u4eec\u8bc1\u660e\u8fd9\u4e2a\u56fe\u903c\u8fd1\u4e8e\u4e0a\u9762\u7684\u56fe\uff0c\u8fd9\u4e24\u4e2a\u56fe\u90fd\u7f16\u7801\u4e00\u4e2a\u5927\u5230\u4e0d\u53ef\u80fd\u4e3a\u771f\u7684\u9634\u8c0b\u3002| \u6765\u6e90\uff1aSamuel Velasco\/Quanta Magazine<\/span><\/section>\n


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\u91cd\u590d\u8fd9\u4e2a\u8fc7\u7a0b\u51e0\u6b21\u5e76\u4e0d\u660e\u663e\u80fd\u5bfc\u5411\u7ed9\u5b9a\u90bb\u57df\u4e2d\u7684\u4efb\u4f55\u70b9\uff0c\u4f46\u5982\u679c\u56fe\u771f\u7684\u662f\u6269\u5c55\u56fe\uff0c\u60c5\u51b5\u5e94\u8be5\u662f\u8fd9\u6837\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5f53\u56fe\u4e0a\u7684\u6574\u6570\u53d8\u5f97\u8db3\u591f\u5927\u65f6\uff0c\u751a\u81f3\u8fde\u968f\u673a\u8def\u5f84\u5982\u4f55\u521b\u5efa\u90fd\u4e0d\u518d\u6e05\u695a\uff1a\u5c06\u6570\u5b57\u5206\u89e3\u4e3a\u5b83\u4eec\u7684\u8d28\u56e0\u6570\uff0c\u4ece\u800c\u5b9a\u4e49\u56fe\u7684\u8fb9\uff0c\u53d8\u5f97\u5f02\u5e38\u56f0\u96be\u3002\u201c\u8ba1\u7b97\u6240\u6709\u8fd9\u4e9b\u6e38\u8d70\uff0c\u4f1a\u662f\u4e00\u4ef6\u53ef\u6015\u7684\u4e8b\u60c5\u3002\u201d Helfgott \u8bf4\u3002<\/span><\/p>\n


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\u5f53\u9676\u54f2\u8f69\u8bd5\u56fe\u8bc1\u660e\u4ed6\u7684\u56fe\u662f\u4e00\u4e2a\u6269\u5c55\u56fe\u65f6\uff0c\u201c\u8fd9\u6709\u70b9\u592a\u96be\u4e86\uff0c\u201d\u4ed6\u8bf4\u3002\u4e0d\u8fc7\u4ed6\u5f00\u53d1\u4e86\u4e00\u79cd\u65b0\u65b9\u6cd5\uff0c\u57fa\u4e8e\u71b5\u8fd9\u79cd\u5bf9\u968f\u673a\u6027\u7684\u5ea6\u91cf\u3002\u8fd9\u4f7f\u4ed6\u80fd\u591f\u907f\u514d\u5c55\u793a\u6269\u5c55\u56fe\u5c5e\u6027\u7684\u9700\u8981\u2014\u2014\u4f46\u9700\u8981\u4ed8\u51fa\u4ee3\u4ef7\u3002\u4ed6\u53ef\u4ee5\u89e3\u51b3\u5bf9\u6570\u4e54\u62c9\u731c\u60f3\uff0c\u4f46\u4e0d\u5982\u4ed6\u60f3\u7684\u90a3\u4e48\u7cbe\u786e\u3002\u5728\u731c\u60f3\u7684\u7406\u60f3\u8bc1\u660e\u4e2d\uff0c\u6574\u6570\u4e4b\u95f4\u7684\u5947\u5076\u72ec\u7acb\u6027\u5e94\u8be5\u603b\u662f\u5f88\u660e\u663e\uff0c\u5373\u4f7f\u6cbf\u7740\u6570\u8f74\u7684\u4e00\u5c0f\u90e8\u5206\u3002\u4f46\u662f\u5728\u9676\u54f2\u8f69\u7684\u8bc1\u660e\u4e2d\uff0c\u76f4\u5230\u91c7\u6837\u4e86\u5929\u6587\u6570\u5b57\u91cf\u7ea7\u7684\u6574\u6570\uff0c\u8fd9\u79cd\u72ec\u7acb\u6027\u624d\u53d8\u5f97\u660e\u6717<\/strong>\u3002\u201c\u91cf\u5316\u6765\u770b\uff0c\u5b83\u4e0d\u662f\u5f88\u5f3a\u5927\u3002\u201d\u56fe\u5c14\u5e93\u5927\u5b66\u7684 Joni Ter\u00e4v\u00e4inen \u8bf4\u3002<\/span><\/p>\n


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\u6b64\u5916\uff0c\u4ed6\u7684\u71b5\u65b9\u6cd5\u5982\u4f55\u6269\u5c55\u5230\u5176\u5b83\u95ee\u9898\u4e0a\u4ecd\u7136\u4e0d\u6e05\u695a\u3002\u725b\u6d25\u5927\u5b66\u7684 James Maynard \u8bf4\uff0c\u201c\u9676\u54f2\u8f69\u7684\u5de5\u4f5c\u662f\u4e00\u4e2a\u5f7b\u5e95\u7684\u7a81\u7834\uff0c\u201d\u4f46\u7531\u4e8e\u8fd9\u4e9b\u9650\u5236\uff0c\u201c\u5b83\u4e0d\u53ef\u80fd\u7ed9\u51fa\u66f4\u591a\u4e1c\u897f\u81ea\u7136\u5f15\u5bfc\u6211\u4eec\u5230\u95ee\u9898\u7684\u4e0b\u4e00\u6b65\uff0c\u6bd4\u5982\u5b6a\u751f\u8d28\u6570\u731c\u60f3\u3002\u201d<\/span><\/p>\n


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\u4e94\u5e74\u540e\uff0cHelfgott \u548c Radziwi\u0142\u0142 \u8bbe\u6cd5\u505a\u5230\u4e86\u9676\u54f2\u8f69\u65e0\u6cd5\u505a\u5230\u7684\u4e8b\u60c5\u2014\u2014\u8fdb\u4e00\u6b65\u6269\u5927\u4ed6\u53d1\u73b0\u7684\u9634\u8c0b\u3002<\/span><\/p>\n


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\u56fe7. Maksym Radziwi\u0142\u0142\uff08\u5de6\uff09\u548c Harald Helfgott\uff08\u53f3\uff09\u7814\u7a76\u4e86\u6269\u5c55\u56fe\u4e0a\u7684\u968f\u673a\u6e38\u8d70\uff0c\u4ee5\u8bc1\u660e\u5173\u4e8e\u8fde\u7eed\u6574\u6570\u7684\u8d28\u56e0\u6570\u5206\u89e3\u7684\u5f3a\u9648\u8ff0\u3002| \u6765\u6e90\uff1a\u52a0\u5dde\u7406\u5de5\u5b66\u9662\uff1b\u6d2a\u5821\u57fa\u91d1\u4f1a\/Sven M\u00fcller
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Helfgott \u548c Radziwi\u0142\u0142 \u9700\u8981\u8bc1\u660e\u8fd9\u4e2a\u6734\u7d20\u56fe\u903c\u8fd1\u4e8e\u9676\u54f2\u8f69\u7684\u56fe\u3002\u5982\u679c\u4ed6\u4eec\u80fd\u8bc1\u660e\u8fd9\u4e24\u4e2a\u56fe\u662f\u76f8\u4f3c\u7684\uff0c\u5c31\u53ef\u4ee5\u901a\u8fc7\u7814\u7a76\u6734\u7d20\u56fe\u6765\u63a8\u65ad\u9676\u54f2\u8f69\u7684\u56fe\u7684\u5c5e\u6027\u3002\u800c\u4e14\u56e0\u4e3a\u4ed6\u4eec\u5df2\u7ecf\u77e5\u9053\u6734\u7d20\u56fe\u662f\u5c40\u90e8\u6269\u5c55\u56fe\uff0c\u5c31\u53ef\u4ee5\u63a8\u65ad\u9676\u54f2\u8f69\u7684\u56fe\u4e5f\u662f<\/span>\uff08\u56e0\u6b64\u5bf9\u6570\u4e54\u62c9\u731c\u60f3\u4e3a\u771f\uff09<\/span>\u3002<\/span><\/p>\n


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\u4f46\u662f\u8003\u8651\u5230\u8fd9\u4e2a\u6734\u7d20\u56fe\u6bd4\u9676\u54f2\u8f69\u7684\u56fe\u7684\u8fb9\u591a\u5f97\u591a\uff0c\u5982\u679c\u5b58\u5728\u76f8\u4f3c\u4e4b\u5904\uff0c\u5b83\u4e5f\u88ab\u63a9\u57cb\u4e86\u3002\u201c\u5f53\u4f60\u8bf4\u8fd9\u4e9b\u56fe\u770b\u8d77\u6765\u5f88\u50cf\u65f6\uff0c\u8fd9\u5c06\u610f\u5473\u7740\u4ec0\u4e48\uff1f\u201d Helfgott \u8bf4\u3002<\/span><\/p>\n


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\u867d\u7136\u8fd9\u4e24\u79cd\u56fe\u5728\u8868\u9762\u4e0a\u770b\u8d77\u6765\u5e76\u4e0d\u50cf\uff0c\u4f46 Helfgott \u548c Radziwi\u0142\u0142 \u901a\u8fc7\u5728\u4e24\u4e2a\u89c6\u89d2\u4e4b\u95f4\u8f6c\u6362\u6765\u8bc1\u660e\u5b83\u4eec\u5f7c\u6b64\u903c\u8fd1\u3002\u4e00\u65b9\u9762\uff0c\u4ed6\u4eec\u5c06\u56fe\u89c6\u4e3a\u56fe\uff1b\u53e6\u4e00\u65b9\u9762\uff0c\u4ed6\u4eec\u5c06\u56fe\u89c6\u4e3a\u77e9\u9635\u8fd9\u79cd\u6570\u5b66\u5bf9\u8c61\u3002<\/span>
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Helfgott \u548c Radziwi\u0142\u0142 \u9700\u8981\u8bc1\u660e\uff0c\u4e0e\u8be5\u77e9\u9635\u76f8\u5173\u7684\u7279\u5b9a\u53c2\u6570<\/span>\uff08\u79f0\u4e3a\u7279\u5f81\u503c\uff09<\/span>\u90fd\u5f88\u5c0f\u3002\u8fd9\u662f\u56e0\u4e3a\u6269\u5c55\u56fe\u7684\u4e00\u4e2a\u5b9a\u4e49\u7279\u5f81\u662f\u5b83\u7684\u90bb\u63a5\u77e9\u9635\u5177\u6709\u4e00\u4e2a\u5927\u7684\u7279\u5f81\u503c\uff0c\u800c\u5176\u4f59\u7684\u5219\u660e\u663e\u66f4\u5c0f\u3002\u5982\u679c\u9676\u54f2\u8f69\u7684\u56fe\u548c\u6734\u7d20\u56fe\u540c\u6837\u662f\u6269\u5c55\u56fe\uff0c\u90a3\u4e48\u5b83\u4e5f\u4f1a\u6709\u4e00\u4e2a\u5927\u7684\u7279\u5f81\u503c\u2014\u2014\u5f53\u4ece\u4e00\u4e2a\u77e9\u9635\u4e2d\u51cf\u53bb\u53e6\u4e00\u4e2a\u77e9\u9635\u65f6\uff0c\u8fd9\u4e24\u4e2a\u5927\u7684\u7279\u5f81\u503c\u51e0\u4e4e\u4f1a\u62b5\u6d88\uff0c\u7559\u4e0b\u4e00\u7ec4\u90fd\u5f88\u5c0f\u7684\u7279\u5f81\u503c\u3002<\/span><\/p>\n


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\u4f46\u662f\u7279\u5f81\u503c\u672c\u8eab\u5f88\u96be\u7814\u7a76\u3002\u76f8\u53cd\uff0c\u8bc1\u660e\u8be5\u77e9\u9635\u7684\u6240\u6709\u7279\u5f81\u503c\u90fd\u5f88\u5c0f\u7684\u7b49\u6548\u65b9\u6cd5\u53c8\u4f1a\u56de\u5230\u56fe\u8bba\u3002\u56e0\u6b64\uff0cHelfgott \u548c Radziwi\u0142\u0142 \u5c06\u8fd9\u4e2a\u77e9\u9635<\/span>\uff08\u4ee3\u8868\u4ed6\u4eec\u7684\u6734\u7d20\u56fe\u7684\u77e9\u9635\u4e0e\u9676\u54f2\u8f69\u7684\u66f4\u590d\u6742\u7684\u77e9\u9635\u4e4b\u95f4\u7684\u5dee\u5f02\uff09<\/span>\u8f6c\u6362\u56de\u4e86\u4e00\u4e2a\u56fe\u3002\u7136\u540e\uff0c\u4ed6\u4eec\u8bc1\u660e\u8fd9\u4e2a\u56fe\u5305\u542b\u5f88\u5c11\u7684\u4f1a\u5faa\u73af\u56de\u5230\u8d77\u70b9\u7684\u968f\u673a\u6e38\u8d70<\/span>\uff08\u5177\u6709\u7279\u5b9a\u957f\u5ea6\u5e76\u4e14\u7b26\u5408\u5c11\u6570\u5176\u4ed6\u5c5e\u6027\uff09<\/span>\u3002\u8fd9\u610f\u5473\u7740\u9676\u54f2\u8f69\u7684\u56fe\u4e0a\u7684\u5927\u591a\u6570\u968f\u673a\u6e38\u8d70\u57fa\u672c\u4e0a\u62b5\u6d88\u4e86\u6734\u7d20\u6269\u5c55\u56fe\u4e0a\u7684\u968f\u673a\u6e38\u8d70\u2014\u2014\u8fd9\u610f\u5473\u7740\u524d\u8005\u53ef\u4ee5\u88ab\u540e\u8005\u903c\u8fd1\uff0c\u56e0\u6b64\u4e24\u8005\u90fd\u662f\u6269\u5c55\u56fe\u3002<\/span><\/p>\n


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Helfgott \u548c Radziwi\u0142\u0142 \u5bf9\u5bf9\u6570\u4e54\u62c9\u731c\u60f3\u7684\u89e3\u51b3\u65b9\u6848\u6807\u5fd7\u7740\u5bf9\u9676\u54f2\u8f69\u7ed3\u679c\u7684\u663e\u8457\u91cf\u5316\u6539\u8fdb\u3002\u4ed6\u4eec\u53ef\u4ee5\u5bf9\u66f4\u5c11\u7684\u6574\u6570\u8fdb\u884c\u91c7\u6837\u5c31\u80fd\u5f97\u51fa\u76f8\u540c\u7684\u7ed3\u679c\uff1a\u4e00\u4e2a\u6574\u6570\u7684\u8d28\u56e0\u6570\u6570\u91cf\u7684\u5947\u5076\u6027\u4e0e\u5176\u90bb\u5c45\u7684\u5947\u5076\u6027\u4e0d\u76f8\u5173\u3002<\/span><\/p>\n


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\u725b\u6d25\u5927\u5b66\u7684 Ben Green \u8bf4\uff1a\u201c\u8fd9\u662f\u89e3\u91ca\u8d28\u6570\u548c\u53ef\u9664\u6027\u770b\u8d77\u6765\u4e3a\u4f55\u968f\u673a\u7684\u4e00\u4e2a\u975e\u5e38\u6709\u529b\u7684\u9648\u8ff0\u3002\u201d \u4f46\u8fd9\u9879\u5de5\u4f5c\u53ef\u80fd\u66f4\u4ee4\u4eba\u5174\u594b\uff0c\u56e0\u4e3a\u5b83\u63d0\u4f9b\u4e86\u201c\u4e00\u79cd\u89e3\u51b3\u95ee\u9898\u7684\u81ea\u7136\u65b9\u6cd5\u201d \uff0cMatom\u00e4ki \u8bf4\u2014\u2014\u8fd9\u6b63\u662f\u9676\u54f2\u8f69\u516d\u5e74\u524d\u6700\u521d\u5e0c\u671b\u7684\u76f4\u89c2\u65b9\u6cd5\u3002<\/span><\/p>\n


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\u6269\u5c55\u56fe\u4e4b\u524d\u5df2\u7ecf\u5728\u7406\u8bba\u8ba1\u7b97\u673a\u79d1\u5b66\u3001\u7fa4\u8bba\u548c\u5176\u4ed6\u6570\u5b66\u9886\u57df\u5e26\u6765\u4e86\u65b0\u53d1\u73b0\u3002\u73b0\u5728\uff0cHelfgott \u548c Radziwi\u0142\u0142 \u4e5f\u5c06\u5b83\u4eec\u7528\u4e8e\u6570\u8bba\u95ee\u9898\u3002\u4ed6\u4eec\u7684\u5de5\u4f5c\u8868\u660e\uff0c\u6269\u5c55\u56fe\u6709\u80fd\u529b\u63ed\u793a\u7b97\u672f\u7684\u4e00\u4e9b\u6700\u57fa\u672c\u5c5e\u6027\u2014\u2014\u6d88\u9664\u6f5c\u5728\u7684\u9634\u8c0b\uff0c\u5e76\u5f00\u59cb\u89e3\u5f00\u52a0\u6cd5\u548c\u4e58\u6cd5\u4e4b\u95f4\u590d\u6742\u7684\u76f8\u4e92\u7ea0\u7f20\u3002<\/strong><\/span><\/p>\n


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Maynard \u8bf4\uff1a\u201c\u7a81\u7136\u4e4b\u95f4\uff0c\u5f53\u4f7f\u7528\u56fe\u8fd9\u79cd\u8bed\u8a00\u65f6\uff0c\u5b83\u4f1a\u5728\u95ee\u9898\u4e2d\u770b\u5230\u4f60\u4e8b\u5148\u65e0\u6cd5\u771f\u6b63\u770b\u5230\u7684\u6240\u6709\u8fd9\u4e9b\u7ed3\u6784\u3002\u8fd9\u5c31\u662f\u5965\u5999\u6240\u5728\u3002\u201d<\/span><\/p>\n


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\u53c2\u8003\u8d44\u6599<\/strong><\/span><\/p>\n

[1]  Wolfram Research (2008), Liouville Lambda, Wolfram Language function, https:\/\/reference.wolfram.com\/language\/ref\/LiouvilleLambda.html.<\/span><\/section>\n
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\u539f\u6587\u94fe\u63a5\uff1ahttps:\/\/www.quantamagazine.org\/mathematicians-outwit-hidden-number-conspiracy-20220103\/<\/span><\/section>\n

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\u96c6\u667a\u6591\u56fe\u9876\u520a\u8bba\u6587\u901f\u9012\u680f\u76ee\u4e0a\u7ebf\u4ee5\u6765\uff0c\u6301\u7eed\u6536\u5f55\u6765\u81eaNature\u3001Science<\/span>\u7b49\u9876\u520a\u7684\u6700\u65b0\u8bba\u6587\uff0c\u8ffd\u8e2a\u590d\u6742\u7cfb\u7edf\u3001\u7f51\u7edc\u79d1\u5b66\u3001\u8ba1\u7b97\u793e\u4f1a\u79d1\u5b66\u7b49\u9886\u57df\u7684\u524d\u6cbf\u8fdb\u5c55\u3002\u73b0\u5728\u6b63\u5f0f\u63a8\u51fa\u8ba2\u9605\u529f\u80fd\uff0c\u6bcf\u5468\u901a\u8fc7\u5fae\u4fe1\u670d\u52a1\u53f7\u300c\u96c6\u667a\u6591\u56fe\u300d\u63a8\u9001\u8bba\u6587\u4fe1\u606f\u3002\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\u5373\u53ef\u4e00\u952e\u8ba2\u9605\uff1a<\/span>
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