求证：若a^2+b^2=c^2-1，a,b,c均正整数则a,b必须都是偶数

wayne · 发表于 2012-1-19 22:23:35

再比如：x = 2*7^2*5^4*17^8 ，C=ceil(5*9/2) = 23
Mathematica解得刚好是23组：
{{240737,20668991},{846685,20653045},{1842953,20588071},{2321977,20539561},{2923235,20462645},{3995425,20280575},{4970035,20063995},{5056555,20042365},{6018425,19774825},{7050155,19430915},{7980175,19067825},{8062369,19033217},{8972005,18621715},{9514169,18350633},{9938999,18124057},{10466155,17824835},{11314639,17298673},{11714479,17030447},{12208805,16679635},{12999959,16070663},{13069175,16014425},{13827205,15364685},{14616175,14616175}}

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[讨论] 求证：若a^2+b^2=c^2-1，a,b,c均正整数则a,b必须都是偶数