{"id":521,"date":"2021-03-31T12:00:00","date_gmt":"2021-03-31T04:00:00","guid":{"rendered":"https:\/\/blog.cruciferslab.net\/?p=521"},"modified":"2021-04-05T19:32:14","modified_gmt":"2021-04-05T11:32:14","slug":"project-euler-%e8%a7%a3%e9%a1%8c%e7%ad%86%e8%a8%98-1","status":"publish","type":"post","link":"https:\/\/blog.cruciferslab.net\/?p=521","title":{"rendered":"Project Euler \u89e3\u984c\u7b46\u8a18 (1)"},"content":{"rendered":"\n<p>\u65e2\u7136\u8981\u4f86\u8a18\u89e3\u984c\u7b46\u8a18\u5c31\u4f86\u9806\u4fbf\u8a18\u4e00\u4e0b\u6642\u4e0d\u6642\u6703\u505a\u7684 Project Euler \u597d\u4e86\u3002\u9019\u88e1\u7684\u6587\u7ae0\u61c9\u8a72\u6703\u4e00\u8d77\u6392\u9032\u6163\u4f8b\u7684\u9031\u4e09\u66f4\u65b0\u7576\u4e2d\uff0c\u6240\u4ee5\u770b\u5230\u4e00\u7bc7\u7b46\u8a18\u51fa\u4f86\u4e26\u4e0d\u4ee3\u8868\u6211\u525b\u89e3\u5b8c\u9019\u4e00\u984c\uff0c\u800c\u53ef\u80fd\u662f\u597d\u5e7e\u5929\u524d\u7684\u4e8b\u4e86 XD<\/p>\n\n\n\n<p>\u6211\u505a Project Euler \u4e3b\u8981\u7684\u5de5\u5177\u662f Mathematica\uff0c\u56e0\u70ba\u5f88\u591a\u6578\u5b78\u76f8\u95dc\u7684\u6771\u897f\u53ef\u4ee5\u4e0d\u7528\u6211\u81ea\u5df1\u5beb\uff1b\u53ea\u6709\u5728\u4e00\u4e9b\u8cc7\u6599\u7d50\u69cb\u7528 MMA \u4e0d\u597d\u5beb\u6216\u5f88\u9700\u8981\u6548\u7387\u7684\u6642\u5019\u624d\u6703\u8f49\u7528 C++ \u4f86\u5beb\u7684\u3002\u6211\u7684 PE \u5e33\u865f\u88e1\u767b\u8a18\u7684\u4f7f\u7528\u8a9e\u8a00\u4e5f\u662f Mathematica\u3002<\/p>\n\n\n\n<p>\u53e6\u5916\uff0c\u70ba\u4e86\u5728\u5168\u6587\u7ae0\u6a21\u5f0f\u4e5f\u4f5c\u9ede\u7c21\u55ae\u7684\u9632\u96f7\uff0c\u6bcf\u7bc7\u5728\u8a0e\u8ad6\u7684\u984c\u76ee\u6211\u6703\u653e\u5728\u7e7c\u7e8c\u95b1\u8b80\u4e4b\u4e0a\uff0c\u7136\u5f8c\u5728\u524d\u9762\u5beb\u4e00\u9ede\u9019\u984c\u53ef\u4ee5\u516c\u958b\u7684\u6771\u897f\uff0c\u4f8b\u5982\u7c21\u8a55\u6216\u6211\u6d41\u7ffb\u8b6f\u7b49\uff1b\u5728\u7e7c\u7e8c\u95b1\u8b80\u7684\u524d\u4e00\u6bb5\u6211\u6703\u653e\u4e0a\u6211\u7684 Project Euler \u7c3d\u540d\u5716\uff0c\u90a3\u4e4b\u4e0b\u5c31\u6703\u4f86\u958b\u59cb\u653e\u96f7\u4e86\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><a href=\"https:\/\/projecteuler.net\/problem=168\" data-type=\"URL\" data-id=\"https:\/\/projecteuler.net\/problem=168\">#168 &#8211; Number Rotations<\/a> (\u96e3\u5ea6 65%)<\/h2>\n\n\n\n<p>\u7c21\u8ff0\u9019\u984c\u662f\u9019\u6a23\u7684\uff1a<br>142857 \u9019\u500b\u6578\u5b57\uff0c\u5c07\u5176\u500b\u4f4d\u6578\u653e\u5230\u6700\u524d\u9762 (\u7a31\u70ba\u5176\u53f3\u65cb\u8f49) \u5f97\u5230 714285\uff0c\u800c\u6211\u5011\u767c\u73fe 714285 \u662f 142857 \u7684 5 \u500d\u6574\u3002\u8a66\u554f\uff0c\u6240\u6709\u5177\u6709\u6b64\u7a2e\u6027\u8cea\uff0d\uff0d\u4e00\u6578\u70ba\u5176\u53f3\u65cb\u8f49\u7684\u56e0\u6578\uff0d\uff0d\u4e26\u4e14\u5728 10 \u5230 10<sup>100<\/sup> \u4e4b\u9593\u7684\u6578\u7684\u7e3d\u548c\uff0c\u5176\u672b\u4e94\u4f4d\u662f\u591a\u5c11\uff1f<\/p>\n\n\n\n<p>\u9019\u984c\u5176\u5be6\u5f88\u4e45\u4ee5\u524d\u89e3\u904e\uff0c\u4f46\u56e0\u70ba\u5c11\u8003\u616e\u4e86\u4e00\u500b\u6771\u897f\u6240\u4ee5 WA \u4e86\u4e0d\u5c11\u6b21\uff0c\u5c31\u88ab\u6211\u653e\u8457\u4e86\u3002\u6700\u8fd1\u56de\u4f86\u91cd\u65b0\u601d\u8003\u624d\u767c\u73fe\u6211\u5c11\u8003\u616e\u7684\u6771\u897f\u662f\u4ec0\u9ebc\uff0d\uff0d\u800c\u8aaa\u4f86\u6709\u8da3\uff0c\u984c\u76ee\u7528 142857 \u8209\u4f8b\u6b63\u662f\u8b93\u6211\u6389\u9032\u9019\u500b\u9677\u9631\u7684\u5143\u5147 XD<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/projecteuler.net\/profile\/progheal.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<!--more-->\n\n\n\n<p>\u5c31\u4f86\u8a8d\u771f\u7b97\u4e00\u4e0b\u5230\u5e95\u662f\u4ec0\u9ebc\u6a23\u7684\u6578\u6709\u9019\u7a2e\u6027\u8cea\u597d\u4e86\u3002\u4ee4 \\(10a+b\\) \u662f\u6211\u5011\u8981\u627e\u7684\u6578\uff0c\u5b83\u6709 \\(n+1\\) \u4f4d\u6578\uff0c\u4e14 \\(0\\leq b\\leq9\\)\u3002\u90a3\u9019\u500b\u6027\u8cea\u53ef\u4ee5\u8868\u793a\u6210\uff1a\u5b58\u5728\u6b63\u6574\u6578 \\(k\\) \u6eff\u8db3 \\(k(10a+b)=b\\cdot10^n+a\\)\u3002\u6574\u7406\u4e00\u4e0b\u53ef\u5f97 $$a\\cdot(10k-1)=b\\cdot(10^n-k)\\\\a:b=(10^n-k):(10k-1)$$ \u6211\u5011\u8981\u627e\u7684 \\(a\\) \u548c \\(b\\) \u986f\u7136\u662f\u6574\u6578\uff0c\u4f46\u662f\u5c0d \\(k\\geq2\\) \u7684\u72c0\u6cc1 \\(10k-1\\) \u4e0d\u662f\u4e00\u4f4d\u6578\uff0c\u56e0\u6b64\u6211\u5011\u6703\u9700\u8981\u9019\u500b\u6bd4\u80fd\u5920\u7d04\u5206\uff0c\u624d\u80fd\u627e\u51fa\u6211\u5011\u8981\u7684 \\(a\\) \u548c \\(b\\) \u4f86\u3002\u96d6\u7136\u984c\u76ee\u6c92\u6709\u660e\u5beb\u8457\u9650\u5236\u9019\u500b\u500d\u6578 \\(k\\) \u7684\u7bc4\u570d\uff0c\u4f46\u5176\u5be6\u96b1\u85cf\u8457\u662f\u6709\u4e00\u500b\u9650\u5236\u5728\u7684\uff1a\u4e0d\u53ef\u80fd\u662f 10 \u500d\u6216\u4ee5\u4e0a\uff1b\u5176\u539f\u56e0\u662f\uff1a\u56e0\u70ba\u6210\u70ba\u500d\u6578\u7684\u6578\u662f\u539f\u6578\u7684\u53f3\u65cb\u8f49\uff0c\u9019\u5169\u500b\u7684\u4f4d\u6578\u76f8\u540c\uff0c\u56e0\u6b64\u76f8\u9664\u7684\u7b54\u6848\u4e0d\u53ef\u80fd\u8d85\u904e 10\u3002<\/p>\n\n\n\n<p>\u4ee5\u984c\u76ee\u8209\u4f8b\u7684 142857 \u4f86\u8aaa\uff0c\u9019\u500b\u72c0\u6cc1\u88e1 \\(a=14285, b=7, k=5, n=5\\)\uff1b\u6211\u5011\u6709 $$(10^n-k):(10k-1)=(10^5-5):49=99995:49=14285:7$$ \u6eff\u8db3\u689d\u4ef6\u3002<\/p>\n\n\n\n<p>\u81ea\u7136\u5730\uff0c\u8981\u627e\u51fa\u6240\u6709\u89e3\u5c31\u662f\u5f9e\u4e0a\u9762\u9019\u689d\u95dc\u4fc2\u5f0f\u51fa\u767c\uff0c\u53bb\u627e \\(10^n-k\\) \u662f \\(10k-1\\) \u500d\u6578\u7684\u6240\u6709 \\(n\\) \u51fa\u4f86\u3002\u9019\u662f\u6240\u8b02\u7684<a href=\"https:\/\/en.wikipedia.org\/wiki\/Discrete_logarithm\" data-type=\"URL\" data-id=\"https:\/\/en.wikipedia.org\/wiki\/Discrete_logarithm\">\u96e2\u6563\u5c0d\u6578\u554f\u984c<\/a>\uff1a\u6211\u5011\u60f3\u627e\u6eff\u8db3 \\(10^n\\equiv k\\mod (10k-1)\\) \u7684\u89e3 \\(n\\)\u3002\u9019\u500b\u554f\u984c\u76ee\u524d\u4e26\u6c92\u6709\u591a\u9805\u5f0f\u89e3\uff0c\u56e0\u6b64\u55ae\u7d14\u5730\u8a66\u904e\u6240\u6709 \\(n\\) \u7684\u507d\u591a\u9805\u5f0f\u89e3\u5c31\u5df2\u7d93\u8db3\u5920\u4f7f\u7528\u4e86\u3002<\/p>\n\n\n\n<p>\u4e0b\u4e00\u500b\u554f\u984c\u662f\uff1a\u5982\u679c \\(10k-1\\) \u4e0d\u662f\u8cea\u6578\u7684\u8a71\uff0c\u6709\u53ef\u80fd\u4e0a\u5f0f\u7d04\u4e00\u534a\u5c31\u53ef\u4ee5\u6709\u8b93 \\(b\\) \u662f\u4e00\u4f4d\u6578\u7684\u89e3\u4e86\u3002\u9019\u5176\u5be6\u62ff\u984c\u76ee\u8209\u7684\u4f8b\u5b50\u5c31\u53ef\u4ee5\u770b\u5f97\u51fa\u4f86\uff1a\u5c0d \\(k=5\\) \u53bb\u6c42\u6a21 49 \u7684\u8a71\uff0c\u6703\u6c42\u5f97 \\(10^{41}\\equiv5\\mod 49\\)\uff1b\u4f46\u82e5\u662f\u53ea\u8981\u6c42\u6a21 7 \u7684\u8a71\uff0c\u5c31\u80fd\u6c42\u5f97\u7bc4\u4f8b\u7684 \\(10^{5}\\equiv5\\mod 7\\)\u3002\u4e0d\u904e\u9019\u4e26\u4e0d\u662f\u554f\u984c\uff0c\u56e0\u70ba\u6211\u5011\u9019\u6a23\u53ea\u6709\u6c42\u51fa \\(n\\)\uff0c\u4e26\u6c92\u6709\u5be6\u969b\u6c42\u51fa \\(a\\) \u548c \\(b\\) \u4f86\uff1b\u63a5\u4e0b\u4f86\u9084\u662f\u5f97\u8981\u7b97\u51fa \\(\\frac{10^n-k}{10k-1}\\)\u662f\u591a\u5c11\uff0c\u518d\u5217\u51fa\u6240\u6709\u6bd4\u4f8b\u76f8\u540c\u7684\u500d\u6578\u51fa\u4f86\u3002\u5c31\u4f86\u5217\u51fa\u9019\u500b\u5927\u6578\u5427\uff1a$$\\frac{10^{41}-5}{49}=2,040,816,326,530,612,244,897,959,183,673,469,387,755$$ \u5b83\u5c0d\u61c9 \\(b=1\\)\uff0c\u4e5f\u5c31\u662f\u5b83\u5c3e\u5df4\u9ecf\u500b 1 \u5c31\u662f\u300c\u7b54\u6848\u300d\u3002\u986f\u7136\u9019\u88e1\u4e58\u4ee5 1 \u5230 9 \u90fd\u662f\u53ef\u80fd\u7684 (a,b) \u89e3\uff0c\u6240\u4ee5\u9019\u88e1\u7684\u300c\u7b54\u6848\u300d\u6709\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>20,408,163,265,306,122,448,979,591,836,734,693,877,551<\/li><li>40,816,326,530,612,244,897,959,183,673,469,387,755,102<\/li><li>61,224,489,795,918,367,346,938,775,510,204,081,632,653<\/li><li>81,632,653,061,224,489,795,918,367,346,938,775,510,204<\/li><li>102,040,816,326,530,612,244,897,959,183,673,469,387,755<\/li><li>122,448,979,591,836,734,693,877,551,020,408,163,265,306<\/li><li>142,857,142,857,142,857,142,857,142,857,142,857,142,857<\/li><li>163,265,306,122,448,979,591,836,734,693,877,551,020,408<\/li><li>183,673,469,387,755,102,040,816,326,530,612,244,897,959<\/li><\/ul>\n\n\n\n<p>\u9019\u88e1\u6211\u5011\u770b\u5230\u4e86\u719f\u6089\u7684 142,857 \u4ee5\u91cd\u8986\u4e86\u4e03\u6b21\u7684\u5f62\u5f0f\u51fa\u73fe\u5728\u9019\u88e1\u4e86\u3002\u4e5f\u5c31\u662f\u8aaa\uff0c\u5c31\u7b97\u5148\u9664\u4e86 49 \u627e\u6b21\u65b9\uff0c\u4f46\u53ea\u8981\u4e58\u4e0a 7 \u500d\u9084\u662f\u80fd\u627e\u5f97\u5230\u9664\u4ee5 7 \u80fd\u627e\u5230\u7684\u7b54\u6848\u7684 (\u56e0\u70ba\u500b\u4f4d\u5c31\u662f 7 \u561b)\u3002\u4e0d\u904e\u9019\u88e1\u9084\u6709\u53e6\u4e00\u500b\u554f\u984c\uff1a\u9019\u4e5d\u500b\u6578\u4e2d\u524d\u9762\u56db\u500b\u6578\u5176\u5be6\u4e26\u4e0d\u6eff\u8db3\u984c\u610f\u3002\u5c31\u62ff\u7b2c\u4e00\u500b\u4f86\u8aaa\u5427\uff0c\u5b83\u7684 \\(k=5\\) \u500d\u662f\u4e0a\u9762\u7684\u7b2c\u4e94\u500b\u6578\uff0c\u53ef\u4ee5\u770b\u5230\u9019\u4e26\u4e0d\u662f\u76f4\u63a5\u7684\u53f3\u65cb\u8f49\uff0c\u800c\u662f\u8981\u5728\u4e2d\u9593\u63d2\u5165\u4e00\u500b 0\u3002\u539f\u56e0\u5f88\u7c21\u55ae\uff1a\\(10k-1\\) \u662f\u5169\u4f4d\u6578\u3002\u7531\u65bc \\(a\\) \u7684\u503c\u662f \\(\\frac{10^n-k}{10k-1}\\)\uff0c\u5341\u500d\u52a0 1 \u6703\u5f97\u5230\u4e00\u500b\u7d04\u7565\u662f \\(\\frac{10^n}{k}\\) \u7684\u6578\uff0c\u5c0f\u65bc \\(10^n\\) \u56e0\u6b64\u4e0d\u8db3 \\(n+1\\) \u4f4d\u3002\u4e0d\u904e\u65e2\u7136\u77e5\u9053\u5927\u7565\u662f\u591a\u5c11\uff0c\u4e5f\u5c31\u77e5\u9053\u53ea\u8981\u4e58\u4ee5\u81f3\u5c11 \\(k\\) \u500d\u5c31\u6703\u662f\u4f4d\u6578\u8db3\u5920\u7684\u7b54\u6848\u4e86\u3002<\/p>\n\n\n\n<p>\u9019\u88e1\u5c31\u53ef\u4ee5\u4f86\u63d0\u4e00\u4e0b\u6211\u5f88\u4e45\u4ee5\u524d\u88ab\u8aa4\u5c0e\u7684\u662f\u4ec0\u9ebc\u4e86\uff1a\u7576\u6642\u7684\u6211\u6c92\u6709\u89c0\u5bdf\u5230\u4e0a\u9762\u5169\u4ef6\u4e8b\uff0c\u56e0\u6b64\u64c5\u81ea\u8a8d\u5b9a \\(k=5\\) \u7684\u72c0\u6cc1\u7279\u6b8a\u5230\u53ea\u6709 142857 \u662f\u7b54\u6848\uff0c\u6240\u4ee5\u6f0f\u7b97\u4e86\u4e0a\u9762\u5217\u8868\u4e2d\u80fd\u7576\u7b54\u6848\u7684\u4e94\u500b\u6578\u4e2d\u7684\u56db\u500b\u2026\u2026 orz<\/p>\n\n\n\n<p>\u4e0a\u9762\u9019\u7d44\u91cd\u8986\u4e86\u4e03\u6b21\u7684 142857 \u4e5f\u544a\u8a34\u4e86\u6211\u5011\u53e6\u4e00\u4ef6\u91cd\u8981\u7684\u4e8b\uff1a\u5982\u679c\u4e00\u500b\u6578\u662f\u7b54\u6848\uff0c\u90a3\u9019\u500b\u6578\u91cd\u8986\u4efb\u610f\u591a\u6b21\u5408\u4f75\u8d77\u4f86\u4e5f\u662f\u7b54\u6848\uff1b\u7406\u7531\u5f88\u7c21\u55ae\uff0c\u60f3\u50cf\u4e00\u4e0b\u76f4\u5f0f\u4e58\u6cd5\u5c31\u597d\u3002\u56e0\u6b64\u6211\u5011\u53ea\u8981\u5c0d\u6240\u6709\u9019\u6a23\u627e\u51fa\u4f86\u4f4d\u6578\u7b26\u5408\u7684\u4f4d\u6578\uff0c\u7b97\u4e00\u4e0b 100 \u4f4d\u53ef\u4ee5\u64fa\u591a\u5c11\u6b21\uff0c\u628a\u5f8c\u4e94\u4f4d\u4e58\u4e0a\u90a3\u9ebc\u591a\u6b21\u7d2f\u8a08\u8d77\u4f86\u5c31\u597d\u4e86\u3002\u5e78\u904b\u5730\u6240\u6709\u9019\u4e9b\u6578\u90fd\u81f3\u5c11\u516d\u4f4d\uff0c\u6240\u4ee5\u76f4\u63a5\u53d6\u6a21 10<sup>5<\/sup> \u5c31\u884c\u4e86\u3002<\/p>\n\n\n\n<p>But wait, there&#8217;s more!<\/p>\n\n\n\n<p>\u5f9e\u958b\u7bc7\u5230\u73fe\u5728\u6211\u6709\u4e00\u500b\u8a0e\u8ad6\u524d\u63d0\u53ea\u6709\u63d0\u904e\u4e00\u6b21\uff1a\\(k\\geq2\\)\u3002<br>\\(k=1\\) \u7684\u72c0\u6cc1\u7a0d\u5fae\u5730\u4e0d\u592a\u4e00\u6a23\uff1a\u5982\u679c\u53bb\u89e3\u90a3\u500b\u6bd4\u7684\u8a71\uff0c\u56e0\u70ba \\(10k-1=9\\)\uff0c\u6240\u6709\u6574\u6578 \\(n\\) \u90fd\u6703\u6eff\u8db3 \\(10^n-1=999&#8230;999\\) \u662f 9 \u7684\u500d\u6578\u3002\u4e00\u9664\u5c31\u77e5\u9053 \\(a\\) \u662f\u500b\u5168\u90e8\u90fd\u662f 1 \u7684 <a href=\"https:\/\/zh.wikipedia.org\/wiki\/%E7%B4%94%E4%BD%8D%E6%95%B8\" data-type=\"URL\" data-id=\"https:\/\/zh.wikipedia.org\/wiki\/%E7%B4%94%E4%BD%8D%E6%95%B8\">repdigit<\/a>\uff0c\u4e58\u4e0a\u500b\u4f4d\u6578\u4f4d\u6578\u5c31\u8868\u793a\u6240\u6709 repdigit \u90fd\u662f\u7b54\u6848\uff0d\uff0d\u4e0d\u904e\u7528\u770b\u7684\u4e5f\u770b\u5f97\u51fa\u4f86 \\(k=1\\) \u500d\u7684\u6578\u5c31\u662f\u6240\u6709\u7684 repdigit\u3002\u5b83\u5011\u90fd\u662f\u7b54\u6848\u7684\u554f\u984c\u5728\u65bc\uff0c\u6211\u5011\u4e0d\u80fd\u7528\u55ae\u4e00\u89e3\u53d6\u5f8c\u4e94\u4f4d\uff0c\u56e0\u70ba\u9019\u662f\u50c5\u6709\u7684\u4e00\u500b \\(a\\) \u9664\u51fa\u4f86\u4e0d\u8db3\u4e94\u4f4d\u7684\u72c0\u6cc1 (\\(a=1\\))\uff1b\u4e0d\u904e\u56e0\u70ba\u4e5f\u5c31\u50c5\u6709\u9019\u4e00\u500b\uff0c\u53ea\u8981\u53e6\u5916\u7b97\u51fa\u4f86\u518d\u52a0\u9032\u53bb\u5c31\u884c\u4e86\uff0d\uff0d\u81f3\u5c11\u4e94\u4f4d\u7684\u72c0\u6cc1\u6709 96 \u7a2e\uff0c\u7136\u5f8c\u518d\u7b97\u5165 11, 111, 1111, \u6240\u4ee5 repdigit 1 \u7e3d\u548c\u7684\u5f8c\u4e94\u4f4d\u662f \\(11111\\times96+1233\\equiv67889\\mod10^5\\)\uff1b\u5176\u4ed6 repdigit \u985e\u63a8\u5373\u53ef\u3002\u628a\u9019\u4e9b\u5168\u90e8\u52a0\u7e3d\u8d77\u4f86\u624d\u662f\u6700\u7d42\u7684\u7b54\u6848\u3002\u5be6\u969b\u7b54\u6848\u662f\u591a\u5c11\u907f\u514d\u76f4\u63a5\u7206\u7b54\u6848\u7684\u96f7\u5c31\u4e0d\u5728\u9019\u88e1\u5beb\u51fa\u4f86\u4e86\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u65e2\u7136\u8981\u4f86\u8a18\u89e3\u984c\u7b46\u8a18\u5c31\u4f86\u9806\u4fbf\u8a18\u4e00\u4e0b\u6642\u4e0d\u6642\u6703\u505a\u7684 Project Euler \u597d\u4e86\u3002\u9019\u88e1\u7684\u6587\u7ae0\u61c9\u8a72\u6703\u4e00\u8d77\u6392\u9032\u6163\u4f8b\u7684 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,3,4],"tags":[],"class_list":["post-521","post","type-post","status-publish","format-standard","hentry","category-projecteuler","category-math","category-programming"],"_links":{"self":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/521","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=521"}],"version-history":[{"count":41,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/521\/revisions"}],"predecessor-version":[{"id":573,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/521\/revisions\/573"}],"wp:attachment":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=521"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=521"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=521"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}