{"id":155,"date":"2019-04-27T21:26:19","date_gmt":"2019-04-27T13:26:19","guid":{"rendered":"https:\/\/blog.indeex.club\/?p=155"},"modified":"2020-06-20T23:16:07","modified_gmt":"2020-06-20T15:16:07","slug":"%e5%87%a0%e4%b8%aa%e6%9c%89%e8%b6%a3%e7%9a%84%e6%95%b0%e5%ad%a6%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/blog.indeex.club\/index.php\/2019\/04\/27\/%e5%87%a0%e4%b8%aa%e6%9c%89%e8%b6%a3%e7%9a%84%e6%95%b0%e5%ad%a6%e9%97%ae%e9%a2%98\/","title":{"rendered":"\u51e0\u4e2a\u6709\u8da3\u7684\u6570\u5b66\u95ee\u9898"},"content":{"rendered":"

\u95ee\u9898\uff1a\u627e\u51fa\u6240\u6709\u4f7f\u5f97 2n – 1 \u80fd\u88ab 7 \u6574\u9664\u7684\u6b63\u6574\u6570 n \u3002<\/h4>\n

\u7b54\u6848\uff1a\u7531\u4e8e 2n \u7684\u4e8c\u8fdb\u5236\u8868\u8fbe\u4e3a 1000\u202600 \uff08n \u4e2a 0\uff09\uff0c\u56e0\u6b64 2n – 1 \u7684\u4e8c\u8fdb\u5236\u8868\u8fbe\u4e3a 111\u202611 \uff08n \u4e2a 1\uff09\u3002\u800c 7 \u7684\u4e8c\u8fdb\u5236\u8868\u8fbe\u662f 111 \uff0c\u8981\u60f3\u8ba9\u5b83\u6574\u9664 n \u4e2a 1 \uff0c\u663e\u7136 n \u5fc5\u987b\u662f\u4e5f\u53ea\u80fd\u662f 3 \u7684\u500d\u6570\u3002<\/p>\n

\u95ee\u9898\uff1a\u662f\u5426\u5b58\u5728 100 \u4e2a\u6570\uff0c\u4f7f\u5f97\u5b83\u4eec\u7684\u548c\u7b49\u4e8e\u5b83\u4eec\u7684\u6700\u5c0f\u516c\u500d\u6570\uff1f<\/h4>\n

\u7b54\u6848\uff1a\u5b58\u5728\u3002\u8003\u8651 3, 2 \u00d7 3, 2 \u00d7 32 , 2 \u00d7 33, \u2026, 2 \u00d7 398, 399 \uff0c\u5b83\u4eec\u7684\u548c\u4e3a\uff1a<\/p>\n

\u3000  3 + 2 \u00d7 3 + 2 \u00d7 32 + 2 \u00d7 33 + \u2026 + 2 \u00d7 398 + 399\n  = 3 \u00d7 (1 + 2) + 2 \u00d7 32 + 2 \u00d7 33 + \u2026 + 2 \u00d7 398 + 399\n  = 32 + 2 \u00d7 32 + 2 \u00d7 33 + \u2026 + 2 \u00d7 398 + 399\n  = 32 \u00d7 (1 + 2) + 2 \u00d7 33 + \u2026 + 2 \u00d7 398 + 399\n  = 33 + 2 \u00d7 33 + \u2026 + 2 \u00d7 398 + 399\n  = ... ...\n  = 399 + 399\n  = 2 \u00d7 399\n<\/code><\/pre>\n
\u800c\u8fd9 100 \u4e2a\u6570\u7684\u6700\u5c0f\u516c\u500d\u6570\u6b63\u662f 2 \u00d7 399 \u3002<\/p>\n
\u95ee\u9898\uff1a\u80fd\u5426\u627e\u51fa 100 \u4e2a\u4e0d\u540c\u7684\u6b63\u6574\u6570\uff0c\u4f7f\u5f97\u5176\u4e2d\u4efb\u610f 2 \u2264 k \u2264 100 \u4e2a\u6570\u7684\u7b97\u672f\u5e73\u5747\u6570\u90fd\u6070\u4e3a\u6574\u6570\u3002<\/h4>\n
\u7b54\u6848\uff1a\u80fd\u3002\u8fd9\u4e2a\u95ee\u9898\u975e\u5e38\u552c\u4eba\uff0c\u5b83\u7684\u7b54\u6848\u5f02\u5e38\u7b80\u5355\uff1a 1 \u00b7 100!, 2 \u00b7 100!, 3 \u00b7 100!, \u2026, 100 \u00b7 100! \u663e\u7136\u6ee1\u8db3\u8981\u6c42\u3002<\/p>\n
\u95ee\u9898\uff1a\u6c42\u8bc1\uff0c\u5b58\u5728\u4efb\u610f\u957f\u7684\u8fde\u7eed\u6b63\u6574\u6570\uff0c\u4f7f\u5f97\u5176\u4e2d\u4efb\u4f55\u4e00\u4e2a\u6570\u90fd\u4e0d\u662f\u8d28\u6570\u7684\u5e42\uff08\u5f53\u7136\u66f4\u4e0d\u80fd\u662f\u8d28\u6570\uff09\u3002<\/h4>\n
\u7b54\u6848\u3002\u6709\u4e00\u4e2a\u7ecf\u5178\u7684\u95ee\u9898\u662f\uff0c\u6c42\u8bc1\u5b58\u5728\u4efb\u610f\u957f\u7684\u8fde\u7eed\u6b63\u6574\u6570\uff0c\u5b83\u91cc\u9762\u4e0d\u5305\u542b\u4efb\u4f55\u8d28\u6570\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u76f8\u90bb\u8d28\u6570\u7684\u95f4\u9694\u53ef\u4ee5\u8fbe\u5230\u4efb\u610f\u5927\u3002\u6784\u9020\u7684\u65b9\u6cd5\u582a\u79f0\u7ecf\u5178\u3002\u663e\u7136 n! + 2 \u662f 2 \u7684\u500d\u6570\uff08\u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u63d0\u51fa\u4e00\u4e2a 2 \u6765\uff09\uff0c n! + 3 \u662f 3 \u7684\u500d\u6570\uff0c\u7b49\u7b49\u3002\u56e0\u6b64\uff0c n! + 2, n! + 3, n! + 4, \u2026, n! + n \u5c31\u662f n – 1 \u4e2a\u8fde\u7eed\u7684\u6b63\u6574\u6570\uff0c\u5176\u4e2d\u4efb\u610f\u4e00\u4e2a\u6570\u90fd\u4e0d\u662f\u8d28\u6570\u3002\u7531\u4e8e n \u53ef\u4ee5\u4efb\u610f\u5927\uff0c\u56e0\u6b64\u8fd9\u4e2a\u6570\u5217\u53ef\u4ee5\u4efb\u610f\u957f\u3002<\/p>\n
\u73b0\u5728\uff0c\u6211\u4eec\u8981\u8bc1\u660e\u7684\u662f\u4e00\u4e2a\u66f4\u5f3a\u7684\u7ed3\u8bba\u3002\u6211\u4eec\u53ef\u4ee5\u628a\u521a\u624d\u7684\u6784\u9020\u65b9\u6848\u7b80\u5355\u5730\u4fee\u6539\u4e00\u4e0b\u3002\u53ea\u9700\u8981\u8003\u8651 (n!)2 + 2, (n!)2 + 3, (n!)2 + 4, \u2026, (n!)2 + n \uff0c\u5219\u5176\u4e2d\u6bcf\u4e00\u4e2a\u6570\u90fd\u4e0d\u662f\u8d28\u6570\u7684\u5e42\u3002\u6bd4\u5982\u8bf4 (n!)2 + 5 \uff0c\u663e\u7136\u5b83\u662f 5 \u7684\u500d\u6570\uff0c\u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u63d0\u51fa\u4e00\u4e2a 5 \u6765\uff1b\u7136\u800c\u63d0\u51fa\u4e00\u4e2a 5 \u4e4b\u540e\u5c06\u4f1a\u5f97\u5230 5 \u00b7 (12 \u00b7 22 \u00b7 32 \u00b7 42 \u00b7 5 \u00b7 62 \u00b7 \u2026 \u00b7 n2 + 1) \uff0c\u62ec\u53f7\u91cc\u7684\u6570\u663e\u7136\u4e0d\u518d\u662f 5 \u7684\u500d\u6570\uff0c\u5b83\u9664\u4ee5 5 \u4f59 1 \u3002<\/p>\n
\u6211\u4eec\u8fd8\u80fd\u7ed9\u51fa\u53e6\u4e00\u79cd\u975e\u5e38\u5de7\u5999\u7684\u6784\u9020\u65b9\u6848\uff0c\u5b83\u80fd\u627e\u51fa n \u4e2a\u4e0d\u542b\u8d28\u6570\u5e42\u7684\u8fde\u7eed\u6b63\u6574\u6570\u6570\u5217\uff0c\u5176\u4e2d n \u53ef\u4ee5\u4efb\u610f\u5927\u3002\u6211\u4eec\u53ea\u9700\u8981\u4fdd\u8bc1\uff0c\u6bcf\u4e2a\u6570\u90fd\u542b\u6709\u81f3\u5c11\u4e24\u4e2a\u4e0d\u540c\u7684\u8d28\u56e0\u6570\u5373\u53ef\u3002\u53d6 2n \u4e2a\u4e0d\u540c\u7684\u8d28\u6570 p1, p2, \u2026, pn, q1, q2, \u2026, qn \uff0c\u663e\u7136 p1 \u00b7 q1, p2 \u00b7 q2, \u2026, pn \u00b7 qn \u662f\u4e24\u4e24\u4e92\u8d28\u7684 n \u4e2a\u6570\u3002\u7531\u4e2d\u56fd\u5269\u4f59\u5b9a\u7406\uff0c\u6211\u4eec\u80fd\u627e\u5230\u4e00\u4e2a\u6b63\u6574\u6570 M \uff0c\u4f7f\u5f97 M \u9664\u4ee5 p1 \u00b7 q1 \u4f59 1 \uff0c\u5e76\u4e14 M \u9664\u4ee5 p2 \u00b7 q2 \u4f59 2 \uff0c\u5e76\u4e14 M \u9664\u4ee5 p3 \u00b7 q3 \u4f59 3 \uff0c\u4e00\u76f4\u5230 M \u9664\u4ee5 pn \u00b7 qn \u4f59 n \u3002\u4e8e\u662f\uff0c M – 1, M – 2, M – 3, \u2026, M – n \u5c31\u662f n \u4e2a\u8fde\u7eed\u7684\u6b63\u6574\u6570\uff0c\u5176\u4e2d\u6bcf\u4e00\u4e2a\u90fd\u542b\u6709\u4e24\u4e2a\u4e0d\u540c\u7684\u8d28\u56e0\u6570\u3002<\/p>\n
\u95ee\u9898\uff1a\u6c42\u8bc1\uff0c\u5bf9\u4e8e\u4efb\u610f\u5927\u7684 n \uff0c\u6211\u4eec\u90fd\u80fd\u591f\u627e\u51fa n \u4e2a\u4e24\u4e24\u4e92\u8d28\u7684\u6570\uff0c\u4f7f\u5f97\u4efb\u610f 2 \u2264 k \u2264 n \u4e2a\u6570\u4e4b\u548c\u90fd\u4e0d\u662f\u8d28\u6570<\/h4>\n
\u7b54\u6848\uff1a\u5982\u679c\u53ea\u8981\u6c42\u4efb\u610f\u591a\u4e2a\u6570\u4e4b\u548c\u90fd\u4e0d\u662f\u8d28\u6570\uff0c\u8fd9\u5f88\u597d\u529e\uff1a\u8ba9\u6240\u6709\u6570\u90fd\u662f\u67d0\u4e2a\u6570\u7684\u500d\u6570\u5373\u53ef\u3002\u4f46\u662f\uff0c\u5982\u679c\u8fd9\u4e9b\u6570\u5fc5\u987b\u4e24\u4e24\u4e92\u8d28\uff0c\u540c\u6837\u7684\u8981\u6c42\u8fd8\u80fd\u529e\u5230\u5417\uff1f\u53ef\u4ee5\u7684\u3002\u8003\u8651 n! + 1, 2 \u00b7 (n!) + 1, 3 \u00b7 (n!) + 1, \u2026, n \u00b7 (n!) + 1 \u8fd9 n \u4e2a\u6570\uff0c\u663e\u7136\u4efb\u610f k \u4e2a\u6570\u4e4b\u548c\u90fd\u662f k \u7684\u500d\u6570\uff0c\u56e0\u800c\u4e0d\u662f\u8d28\u6570\u3002\u4e0b\u9762\u8bf4\u660e\u8fd9 n \u4e2a\u6570\u4e24\u4e24\u4e92\u8d28\u3002\u5047\u8bbe i \u00b7 (n!) + 1 \u548c j \u00b7 (n!) + 1 \u6709\u516c\u5171\u7684\u8d28\u56e0\u6570 p \uff0c\u5176\u4e2d 1 \u2264 i < j \u2264 n \uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u5dee (j – i) \u00b7 (n!) \u4e5f\u80fd\u88ab p \u6574\u9664\uff0c\u8bf4\u660e p \u53ea\u80fd\u662f\u4e0d\u8d85\u8fc7 n \u7684\u8d28\u6570\u3002\u8fd9\u4e0e p \u80fd\u6574\u9664 i \u00b7 (n!) + 1 \u77db\u76fe\u3002<\/p>\n
\u95ee\u9898\uff1a\u8bc1\u660e\uff0c\u5bf9\u4e8e\u4efb\u610f\u6b63\u6574\u6570 n \uff0c\u65b9\u7a0b x2 + y2 = zn \u90fd\u6709\u65e0\u7a77\u591a\u7ec4\u6b63\u6574\u6570\u89e3\u3002<\/h4>\n
\u7b54\u6848\uff1a\u8003\u8651 x + yi = (a + bi)n \uff0c\u5176\u4e2d i \u4e3a\u865a\u6570\u5355\u4f4d\u3002\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u56fa\u5b9a\u7684 n \uff0c\u53ea\u8981 a \u548c b \u90fd\u662f\u6574\u6570\uff0c\u90a3\u4e48\u5c55\u5f00\u540e\u5f97\u5230\u7684 x \u548c y \u4e5f\u90fd\u4e00\u5b9a\u662f\u6574\u6570\u3002\u6211\u4eec\u9009\u53d6\u5145\u5206\u5927\u7684 a \uff0c\u8ba9 a + bi \u7684\u8f90\u89d2\u975e\u5e38\u5c0f\u975e\u5e38\u5c0f\uff08\u5c0f\u4e8e \u03c0\/2 \u7684 n \u5206\u4e4b\u4e00\uff09\uff0c\u4ece\u800c\u8ba9 (a + bi)n \u4e0d\u4f1a\u4e0e\u5750\u6807\u8f74\u91cd\u5408\uff0c\u56e0\u800c\u4fdd\u8bc1 x \u548c y \u90fd\u662f\u975e\u96f6\u6574\u6570\u3002\u7b49\u5f0f\u4e24\u8fb9\u540c\u65f6\u53d6\u6a21\uff0c\u4fbf\u6709 x2 + y2 = (a2 + b2)n<\/p>\n
\u95ee\u9898\uff1a\u6211\u4eec\u628a\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e0a\u6240\u6709\u6a2a\u7eb5\u5750\u6807\u4e92\u8d28\u7684\u6574\u683c\u70b9\uff08\u4e5f\u5c31\u662f\u548c\u539f\u70b9\u7684\u8fde\u7ebf\u4e0d\u7ecf\u8fc7\u5176\u4ed6\u70b9\u7684\u6574\u683c\u70b9\uff09\u53eb\u505a\u201c\u65e2\u7ea6\u683c\u70b9\u201d\u3002\u8bc1\u660e\uff0c\u5bf9\u4e8e\u4efb\u610f\u5927\u7684\u6b63\u6574\u6570 n \uff0c\u603b\u5b58\u5728\u4e00\u4e2a\u6574\u683c\u70b9\uff0c\u5b83\u5230\u4efb\u610f\u65e2\u7ea6\u683c\u70b9\u7684\u8ddd\u79bb\u90fd\u5927\u4e8e n \uff08\u6362\u53e5\u8bdd\u8bf4\uff0c\u65e2\u7ea6\u683c\u70b9\u96c6\u7684\u201c\u7a7a\u6d1e\u201d\u53ef\u4ee5\u8fbe\u5230\u4efb\u610f\u5927\uff09\u3002<\/h4>\n
\u7b54\u6848\uff1a\u5217\u4e00\u5f20 (2n + 1) \u00d7 (2n + 1) \u7684\u8868\uff0c\u6bcf\u4e2a\u683c\u5b50\u91cc\u9762\u586b\u5199\u4e00\u4e2a\u4e0d\u540c\u7684\u8d28\u6570\uff08\u7531\u4e8e\u8d28\u6570\u65e0\u7a77\u591a\uff0c\u8fd9\u662f\u603b\u53ef\u4ee5\u529e\u5230\u7684\uff09\u3002\u73b0\u5728\uff0c\u627e\u51fa\u8fd9\u6837\u7684\u4e00\u4e2a a \uff0c\u5b83\u9664\u4ee5\u7b2c i \u884c\u7684\u8d28\u6570\u603b\u662f\u4f59 i \uff08\u5176\u4e2d – n \u2264 i \u2264 n \uff09\u3002\u627e\u51fa\u8fd9\u6837\u7684\u4e00\u4e2a b \uff0c\u5b83\u9664\u4ee5\u7b2c j \u5217\u7684\u8d28\u6570\u603b\u662f\u4f59 j \uff08\u5176\u4e2d -n \u2264 j \u2264 n\uff09\u3002\u4e2d\u56fd\u5269\u4f59\u5b9a\u7406\u4fdd\u8bc1\u4e86\u8fd9\u6837\u7684 a \u548c b \u662f\u5b58\u5728\u7684\u3002\u4e0b\u9762\u8bf4\u660e\uff0c\u70b9 (a, b) \u6ee1\u8db3\u8981\u6c42\u3002<\/p>\n
\"\u51e0\u4e2a\u6709\u8da3\u7684\u6570\u5b66\u95ee\u9898\"<\/p>\n
\u5047\u5982 (a, b) \u5230 (x, y) \u7684\u8ddd\u79bb\u4e0d\u8d85\u8fc7 n \uff0c\u5219 (a – x)2 + (b – y)2 \u2264 n2 \u3002\u56e0\u800c\uff0c a – x \u548c b – y \u90fd\u5fc5\u987b\u5728 – n \u5230 n \u7684\u8303\u56f4\u5185\u3002\u628a a – x \u7684\u503c\u8bb0\u4f5c i \uff0c\u628a b – y \u7684\u503c\u8bb0\u4f5c j \uff0c\u90a3\u4e48 x \u5c31\u7b49\u4e8e a – i \uff0c y \u5c31\u7b49\u4e8e b – j \uff0c\u7531 a \u3001 b \u7684\u6784\u9020\u53ef\u77e5\uff0c x \u548c y \u90fd\u662f\u8868\u683c\u4e2d\u7b2c i \u884c\u7b2c j \u5217\u7684\u90a3\u4e2a\u8d28\u6570\u7684\u500d\u6570\uff0c\u6545 (x, y) \u4e0d\u662f\u65e2\u7ea6\u683c\u70b9\u3002<\/p>\n
\u95ee\u9898\uff1a\u627e\u51fa\u6240\u6709\u8fd9\u6837\u7684\u6b63\u6574\u6570\u5e8f\u5217 (a1, a2, \u2026, an) \uff0c\u5b83\u4eec\u7684\u548c\u4e3a 2n \uff0c\u4f46\u6211\u4eec\u65e0\u6cd5\u628a\u5b83\u4eec\u5206\u6210\u548c\u76f8\u7b49\u7684\u4e24\u7ec4\u3002<\/h4>\n
\u7b54\u6848\uff1a\u8003\u8651 a1, a2, a1 + a2, a1 + a2 + a3, \u2026, a1 + a2 + a3 + \u2026 + an \uff0c\u9664\u4e86 a1 \u548c a2 \u4ee5\u5916\uff0c\u8fd9\u4e9b\u6570\u9664\u4ee5 n \u7684\u4f59\u6570\u4e0d\u5141\u8bb8\u76f8\u7b49\uff0c\u5426\u5219\u5b83\u4eec\u7684\u5dee\u5c31\u662f n \u7684\u500d\u6570\uff0c\u6211\u4eec\u5c31\u627e\u5230\u4e86\u548c\u4e3a n \u7684\u5b50\u96c6\u3002\u7136\u800c\uff0c\u4e0a\u9762\u4e00\u5171\u6709 n + 1 \u4e2a\u6570\uff0c\u5b83\u4eec\u9664\u4ee5 n \u7684\u4f59\u6570\u5fc5\u7136\u6709\u76f8\u7b49\u7684\uff0c\u56e0\u800c\u4e00\u5b9a\u662f a1 \u548c a2 \u9664\u4ee5 n \u7684\u4f59\u6570\u76f8\u7b49\u3002\u7c7b\u4f3c\u5730\uff0c a2 \u548c a3 \u9664\u4ee5 n \u7684\u4f59\u6570\u4e5f\u76f8\u7b49\uff0c a3 \u548c a4 \u9664\u4ee5 n \u7684\u4f59\u6570\u4e5f\u76f8\u7b49\uff0c\u56e0\u800c\u4e8b\u5b9e\u4e0a\u4ece a1 \u5230 an \u6240\u6709\u7684\u6570\u9664\u4ee5 n \u7684\u4f59\u6570\u90fd\u662f\u76f8\u7b49\u7684\u3002<\/p>\n
\u4f46\u662f\u8fd9 n \u4e2a\u6570\u52a0\u8d77\u6765\u53ea\u6709 2n \uff0c\u53ef\u89c1\u6240\u6709\u7684\u6570\u9664\u4ee5 n \u7684\u4f59\u6570\u53ea\u53ef\u80fd\u90fd\u662f 1 \u6216\u8005\u90fd\u662f 2 \u3002\u4e8e\u662f\u6211\u4eec\u5f97\u5230\u4e86\u6240\u6709\u6ee1\u8db3\u8981\u6c42\u7684\u6570\u5217\uff1a (1, 1, 1, \u2026, 1, n + 1) \uff0c\u4ee5\u53ca (2, 2, 2, \u2026, 2) \u3002\u5176\u4e2d\u540e\u8005\u8981\u6c42 n \u4e3a\u5947\u6570\u3002<\/p>\n
\u95ee\u9898\uff1a\u8bc1\u660e\uff0c\u5b58\u5728\u65e0\u7a77\u591a\u4e2a\u6b63\u6574\u6570\u4e09\u5143\u7ec4 (a, b, c) \uff0c\u4f7f\u5f97 a2 + b2 \u3001 b2 + c2 \u3001 a2 + c2 \u90fd\u662f\u5b8c\u5168\u5e73\u65b9\u6570\u3002<\/h4>\n
\u7b54\u6848\uff1a\u4efb\u53d6\u4e00\u7ec4\u52fe\u80a1\u6570 (x, y, z) \uff0c\u4ee4 a = x|4y2 – z2| \uff0c b = y|4×2 – z2|\uff0c c = 4xyz \u3002\u4e8e\u662f\uff0c<\/p>\n
  a2 + b2 = x2(3y2 - x2)2 + y2(3x2 - y2)2\n             = x6 + 3x2y4 + 3x4y2 + y6\n             =(x2 + y2)3 = (z3)2\n  a2 + c2 = x2(4y2 + z2)2\n  b2 + c2 = y2(4x2 + z2)2\n<\/code><\/pre>\n
\u4ece\u800c a \u3001 b \u3001 c \u6ee1\u8db3\u8981\u6c42\u3002\u7531\u4e8e\u52fe\u80a1\u6570\u6709\u65e0\u7a77\u591a\u7ec4\uff0c\u56e0\u6b64\u6ee1\u8db3\u8981\u6c42\u7684 (a, b, c) \u4e5f\u6709\u65e0\u7a77\u591a\u7ec4\u3002<\/p>\n
\u8fd9\u76f8\u5f53\u4e8e\u7ed9\u51fa\u4e86 Euler \u7816\u5757\uff08\u6240\u6709\u68f1\u957f\u548c\u6240\u6709\u9762\u5bf9\u89d2\u7ebf\u90fd\u662f\u6574\u6570\u7684\u957f\u65b9\u4f53\uff09\u7684\u4e00\u79cd\u6784\u9020\u89e3\u3002\u5f53 (x, y, z) = (3, 4, 5) \u65f6\uff0c\u6211\u4eec\u5c06\u5f97\u5230\u68f1\u957f\u5206\u522b\u4e3a 117 \u3001 44 \u3001 240 \u7684 Euler \u7816\u5757\uff0c\u8fd9\u5c31\u662f\u6700\u5c0f\u7684 Euler \u7816\u5757\uff0c\u5b83\u662f\u7531 Paul Halcke \u5728 1719 \u5e74\u53d1\u73b0\u7684\u3002<\/p>\n
\u5927\u5bb6\u6216\u8bb8\u4f1a\u60f3\uff0c\u6709\u6ca1\u6709\u4ec0\u4e48\u957f\u65b9\u4f53\uff0c\u4e0d\u4f46\u6240\u6709\u68f1\u957f\u548c\u6240\u6709\u9762\u5bf9\u89d2\u7ebf\u90fd\u662f\u6574\u6570\uff0c\u8fde\u4f53\u5bf9\u89d2\u7ebf\u4e5f\u662f\u6574\u6570\u5462\uff1f\u8fd9\u6837\u7684\u957f\u65b9\u4f53\u5c31\u53eb\u505a\u5b8c\u7f8e\u957f\u65b9\u4f53\u3002\u6709\u8da3\u7684\u662f\uff0c\u867d\u7136 Euler \u7816\u5757\u6709\u65e0\u7a77\u591a\u79cd\uff0c\u4f46\u662f\u4eba\u4eec\u76ee\u524d\u8fd8\u6ca1\u6709\u627e\u5230\u54ea\u6015\u4e00\u4e2a\u5b8c\u7f8e\u957f\u65b9\u4f53\u3002\u5b8c\u7f8e\u957f\u65b9\u4f53\u7a76\u7adf\u662f\u5426\u5b58\u5728\uff0c\u76ee\u524d\u4ecd\u7136\u662f\u4e00\u4e2a\u672a\u89e3\u4e4b\u8c1c\u3002<\/p>\n
\u95ee\u9898\uff1a\u8bc1\u660e\uff0c\u82e5\u6b63\u6574\u6570 a \u548c b \u4e92\u8d28\uff0c\u5219 [b \/ a] + [2b \/ a] + [3b \/ a] + \u2026 + [(a – 1) b \/ a] = (a – 1)(b – 1) \/ 2 \u3002\u5176\u4e2d\uff0c [n] \u662f n \u7684\u6574\u6570\u90e8\u5206\uff0c\u5373\u5bf9 n \u53d6\u4e0b\u6574\u3002<\/h4>\n
\u7b54\u6848\uff1a\u6211\u4eec\u5148\u4e3e\u4e00\u4e2a\u4f8b\u5b50\u6765\u8bf4\u660e\u8fd9\u4e2a\u95ee\u9898\u7684\u590d\u6742\u6027\u3002\u6570\u5217 [b \/ a], [2b \/ a], [3b \/ a], \u2026, [(a – 1) b \/ a] \u7684\u89c4\u5f8b\u5e76\u4e0d\u4e00\u5b9a\u975e\u5e38\u660e\u786e\u3002\u4f8b\u5982\uff0c\u5f53 a = 17 \u4e14 b = 12 \u65f6\uff0c [12 \/ 17], [2 \u00b7 12 \/ 17], [3 \u00b7 12 \/ 17], \u2026 [16 \u00b7 12 \/ 17] \u5206\u522b\u4e3a 0, 1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 9, 10, 11 \uff0c\u4f46\u8fd9 16 \u4e2a\u6570\u4e4b\u548c\u4e3a 88 \uff0c\u6b63\u597d\u662f 16 \u548c 11 \u4e58\u79ef\u7684\u4e00\u534a\u3002<\/p>\n
\"\u51e0\u4e2a\u6709\u8da3\u7684\u6570\u5b66\u95ee\u9898\"<\/p>\n
\u7ed3\u8bba\u7684\u8bc1\u660e\u5f88\u6709\u610f\u601d\u3002\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u7684\u7b2c\u4e00\u8c61\u9650\u6446\u653e\u4e00\u4e2a\u5bbd\u4e3a a \uff0c\u9ad8\u4e3a b \u7684\u77e9\u5f62\u3002\u5219 [k \u00b7 b \/ a] \u5c31\u662f\u56fe\u4e2d\u7b2c k \u6761\u7ea2\u8272\u7ad6\u76f4\u7ebf\u4e0a\u7684\u6574\u683c\u70b9\u6570\u76ee\uff0c\u6240\u6709 [k \u00b7 b \/ a] \u4e4b\u548c\u4e5f\u5c31\u662f\u9634\u5f71\u4e09\u89d2\u5f62\u5185\u7684\u6574\u683c\u70b9\u603b\u6570\u3002\u7136\u800c\u7531\u4e8e a \u548c b \u4e92\u8d28\uff0c\u77e9\u5f62\u7684\u5bf9\u89d2\u7ebf\u4e0d\u4f1a\u7ecf\u8fc7\u77e9\u5f62\u5185\u90e8\u7684\u4efb\u4f55\u683c\u70b9\uff0c\u56e0\u6b64\u9634\u5f71\u4e09\u89d2\u5f62\u5185\u7684\u6574\u683c\u70b9\u6570\u5c31\u5e94\u8be5\u662f\u77e9\u5f62\u5185\u7684\u6574\u683c\u70b9\u6570\u7684\u4e00\u534a\uff0c\u5373 (a – 1)(b – 1) \/ 2\u3002<\/p>\n
\u95ee\u9898\uff1a\u82e5\u6b63\u65e0\u7406\u6570 \u03b1 \u548c \u03b2 \u6ee1\u8db3 1 \/ \u03b1 + 1 \/ \u03b2 = 1 \uff0c\u6c42\u8bc1\u6570\u5217 [1 \u00b7 \u03b1], [2 \u00b7 \u03b1], [3 \u00b7 \u03b1], \u2026 \u548c [1 \u00b7 \u03b2], [2 \u00b7 \u03b2], [3 \u00b7 \u03b2], \u2026 \u65e2\u65e0\u91cd\u590d\u53c8\u65e0\u9057\u6f0f\u5730\u5305\u542b\u4e86\u6240\u6709\u7684\u6b63\u6574\u6570\u3002\u8fd9\u91cc [ ] \u540c\u6837\u662f\u53d6\u4e0b\u6574\u7684\u610f\u601d\u3002<\/h4>\n
\u7b54\u6848\uff1a\u8ba9\u6211\u4eec\u5148\u6765\u770b\u4e00\u4e2a\u4f8b\u5b50\u5427\u3002\u8003\u8651\u9ec4\u91d1\u6bd4\u4f8b \u03c6 = (\u221a5 + 1) \/ 2 \u2248 1.618 \uff0c\u6211\u4eec\u6709 1 \/ \u03c6 + 1 \/ (\u03c6 + 1) = 1 \u3002\u6570\u5217 [1 \u00b7 \u03c6], [2 \u00b7 \u03c6], [3 \u00b7 \u03c6], \u2026 \u4e3a 1, 3, 4, 6, 8, 9, 11, 12, 14, 16, 17, \u2026 \uff0c\u800c\u6570\u5217 [1 \u00b7 (\u03c6 + 1)], [2 \u00b7 (\u03c6 + 1)], [3 \u00b7 (\u03c6 + 1)], \u2026 \u5219\u4e3a 2, 5, 7, 10, 13, 15, 18, 20, 23, 26, \u2026 \u3002\u4f60\u4f1a\u53d1\u73b0\uff0c\u524d\u4e00\u4e2a\u6570\u5217\u91cc\u6ca1\u6709\u7684\u6570\uff0c\u6b63\u597d\u90fd\u5728\u540e\u4e00\u4e2a\u6570\u5217\u91cc\uff0c\u800c\u540e\u4e00\u4e2a\u6570\u5217\u91cc\u6ca1\u6709\u7684\u6570\uff0c\u524d\u4e00\u4e2a\u6570\u5217\u91cc\u6b63\u597d\u90fd\u6709\u3002\u4e24\u4e2a\u6570\u5217\u5408\u5728\u4e00\u8d77\uff0c\u5c31\u662f\u6574\u4e2a\u6b63\u6574\u6570\u5e8f\u5217\u3002<\/p>\n
\u8fd9\u4e2a\u5b9a\u7406\u53eb\u505a Beatty-Rayleigh \u5b9a\u7406\uff0c\u5b83\u6709\u5f88\u591a\u79cd\u8bc1\u660e\uff0c\u8fd9\u91cc\u7ed9\u51fa\u4e00\u79cd\u6211\u975e\u5e38\u559c\u6b22\u7684\u8bc1\u660e\uff0c\u5b83\u51fa\u81ea Using your Head is Permitted \u3002<\/p>\n
\u9996\u5148\u6ce8\u610f\u5230\uff0c\u5982\u679c x \u548c y \u90fd\u4e0d\u662f\u6574\u6570\uff0c\u90a3\u4e48 [x] \u4e25\u683c\u5730\u5c0f\u4e8e x \uff0c[y] \u4e25\u683c\u5730\u5c0f\u4e8e y \uff0c\u4ece\u800c [x] + [y] < x + y \u3002\u53e6\u5916\uff0c[x] \u4e00\u5b9a\u4e25\u683c\u5730\u5927\u4e8e x – 1 \uff0c [y] \u4e00\u5b9a\u4e25\u683c\u5730\u5927\u4e8e y – 1 \uff0c\u4ece\u800c [x] + [y] \u4e00\u5b9a\u4e25\u683c\u5730\u5927\u4e8e x + y – 2\u3002\u8fd9\u8bf4\u660e\uff0c\u5f53 x \u548c y \u90fd\u4e0d\u662f\u6574\u6570\u65f6\uff0c [x] + [y] \u5c06\u4ecb\u4e8e x + y – 2 \u548c x + y \u4e4b\u95f4\u3002<\/p>\n
\u56de\u5230\u539f\u95ee\u9898\u3002\u663e\u7136\uff0c\u5728\u7b2c\u4e00\u4e2a\u6570\u5217\u4e2d\uff0c\u5c0f\u4e8e n \u7684\u6b63\u6574\u6570\u6709 [n \/ \u03b1] \u4e2a\u3002\u663e\u7136\uff0c\u5728\u7b2c\u4e8c\u4e2a\u6570\u5217\u4e2d\uff0c\u5c0f\u4e8e n \u7684\u6b63\u6574\u6570\u6709 [n \/ \u03b2] \u4e2a\u3002\u56e0\u6b64\uff0c\u5728\u8fd9\u4e24\u4e2a\u6570\u5217\u4e2d\uff0c\u5c0f\u4e8e n \u7684\u6b63\u6574\u6570\u5171\u6709 [n \/ \u03b1] + [n \/ \u03b2] \u4e2a\u3002\u7531\u4e8e \u03b1 \u548c \u03b2 \u90fd\u662f\u65e0\u7406\u6570\uff0c\u56e0\u6b64 n \/ \u03b1 \u548c n \/ \u03b2 \u4e0d\u53ef\u80fd\u4e3a\u6574\u6570\uff0c\u7531\u521a\u624d\u7684\u7ed3\u8bba\uff0c [n \/ \u03b1] + [n \/ \u03b2] \u4e00\u5b9a\u4ecb\u4e8e n \/ \u03b1 + n \/ \u03b2 – 2 \u548c n \/ \u03b1 + n \/ \u03b2 \u4e4b\u95f4\uff0c\u5373 n – 2 \u548c n \u4e4b\u95f4\u3002\u4f46\u662f\uff0c [n \/ \u03b1] + [n \/ \u03b2] \u662f\u4e2a\u6574\u6570\uff0c\u56e0\u800c\u5b83\u7cbe\u786e\u5730\u7b49\u4e8e n – 1 \u3002<\/p>\n
\u8fd9\u8bf4\u660e\uff0c\u524d n – 1 \u4e2a\u6b63\u6574\u6570\u5728\u4e24\u4e2a\u6570\u5217\u4e2d\u4e00\u5171\u51fa\u73b0\u4e86 n – 1 \u6b21\uff0c\u8fd9\u5bf9\u4e8e\u6240\u6709 n \u90fd\u6210\u7acb\u3002\u4e8e\u662f\uff0c\u6b63\u6574\u6570 1 \u5fc5\u987b\u4e14\u53ea\u80fd\u51fa\u73b0\u5728\u5176\u4e2d\u4e00\u4e2a\u6570\u5217\u4e2d\uff0c\u6b63\u6574\u6570 2 \u5fc5\u987b\u4e14\u53ea\u80fd\u51fa\u73b0\u5728\u5176\u4e2d\u4e00\u4e2a\u6570\u5217\u4e2d\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u6bcf\u4e00\u4e2a\u65b0\u7684\u6b63\u6574\u6570\u90fd\u5fc5\u987b\u4e14\u53ea\u80fd\u51fa\u73b0\u5728\u5176\u4e2d\u4e00\u4e2a\u6570\u5217\u4e2d\u3002<\/p>\n
\u8fd9\u79cd\u53d6\u6574\u51fd\u6570\u7684\u5904\u7406\u6280\u5de7\u4e5f\u53ef\u4ee5\u7528\u5230\u4e0a\u4e00\u4e2a\u95ee\u9898\u91cc\uff1a\u5bf9\u4e0a\u4e00\u4e2a\u95ee\u9898\u91cc\u7684\u6570\u5934\u5c3e\u914d\u5bf9\uff0c\u4f60\u4f1a\u53d1\u73b0\u6bcf\u4e00\u5bf9\u6570\u4e4b\u548c\u90fd\u662f b – 1 \u3002<\/p>\n
\u95ee\u9898\uff1a\u628a 10, 100, 1000, 10000, \u2026 \u5206\u522b\u5199\u6210\u4e8c\u8fdb\u5236\u6570\u548c\u4e94\u8fdb\u5236\u6570\uff1a<\/h4>\n
  \u539f\u6570\u5217\uff1a10, 100, 1000, 10000, 10000, \u2026\n  \u4e8c\u8fdb\u5236\uff1a1010, 1100100, 1111101000, 10011100010000, \u2026\n  \u4e94\u8fdb\u5236\uff1a20, 400, 13000, 310000, 11200000, ...\n<\/code><\/pre>\n
\u4f60\u4f1a\u53d1\u73b0\uff0c\u5bf9\u4e8e\u4efb\u610f\u6b63\u6574\u6570 n > 1 \uff0c\u540e\u4e24\u4e2a\u6570\u5217\u91cc\u6070\u597d\u6709\u4e00\u4e2a\u6570\u662f n \u4f4d\u6570\u3002\u8fd9\u662f\u4e3a\u4ec0\u4e48\uff1f<\/p>\n
\u7b54\u6848\uff1a\u8fd9\u662f Beatty-Rayleigh \u5b9a\u7406\u7684\u4e00\u4e2a\u975e\u5e38\u6f02\u4eae\u7684\u76f4\u63a5\u63a8\u8bba\u3002 10k \u7684\u4e8c\u8fdb\u5236\u8868\u8fbe\u6070\u597d\u6709 [log210k] + 1 \u4f4d\uff0c\u5373 [k \u00b7 log210] + 1 \u4f4d\u300210k \u7684\u4e94\u8fdb\u5236\u8868\u8fbe\u6070\u597d\u6709 [log510k] + 1 \u4f4d\uff0c\u5373 [k \u00b7 log510] + 1 \u4f4d\u3002\u6211\u4eec\u53ea\u9700\u8981\u8bc1\u660e\uff0c\u6570\u5217 [1 \u00b7 log210], [2 \u00b7 log210], [3 \u00b7 log210], \u2026 \u548c [1 \u00b7 log510], [2 \u00b7 log510], [3 \u00b7 log510], \u2026 \u65e2\u65e0\u91cd\u590d\u53c8\u65e0\u9057\u6f0f\u5730\u5305\u542b\u4e86\u6240\u6709\u6b63\u6574\u6570\u3002\u6ce8\u610f\u5230 log210 \u548c log510 \u662f\u4e24\u4e2a\u5012\u6570\u548c\u4e3a 1 \u7684\u65e0\u7406\u6570\uff0c\u7528\u4e00\u4e0b Beatty-Rayleigh \u5b9a\u7406\u5c31\u51fa\u6765\u4e86\u3002<\/p>\n\n
have enjoy! 🧐🧐🧐<\/p>\n
\u4f5c\u8005\uff1aindeex<\/p>\n
\u94fe\u63a5\uff1ahttps:\/\/indeex.cc<\/a><\/p>\n
\u8457\u4f5c\u6743\u5f52\u4f5c\u8005\u6240\u6709\u3002\u5546\u4e1a\u8f6c\u8f7d\u8bf7\u8054\u7cfb\u4f5c\u8005\u83b7\u5f97\u6388\u6743\uff0c\u975e\u5546\u4e1a\u8f6c\u8f7d\u8bf7\u6ce8\u660e\u51fa\u5904\u3002<\/p>\n
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\u95ee\u9898\uff1a\u627e\u51fa\u6240\u6709\u4f7f\u5f97 2n – 1 \u80fd\u88ab 7 \u6574\u9664\u7684\u6b63\u6574\u6570 n \u3002 \u7b54\u6848\uff1a\u7531\u4e8e 2n \u7684\u4e8cRead More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[4],"_links":{"self":[{"href":"https:\/\/blog.indeex.club\/index.php\/wp-json\/wp\/v2\/posts\/155"}],"collection":[{"href":"https:\/\/blog.indeex.club\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.indeex.club\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.indeex.club\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.indeex.club\/index.php\/wp-json\/wp\/v2\/comments?post=155"}],"version-history":[{"count":1,"href":"https:\/\/blog.indeex.club\/index.php\/wp-json\/wp\/v2\/posts\/155\/revisions"}],"predecessor-version":[{"id":160,"href":"https:\/\/blog.indeex.club\/index.php\/wp-json\/wp\/v2\/posts\/155\/revisions\/160"}],"wp:attachment":[{"href":"https:\/\/blog.indeex.club\/index.php\/wp-json\/wp\/v2\/media?parent=155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.indeex.club\/index.php\/wp-json\/wp\/v2\/categories?post=155"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.indeex.club\/index.php\/wp-json\/wp\/v2\/tags?post=155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}