wayne 发表于 2012-1-19 09:57:27

a^2+b^2=N

已知丢番图方程a^2+b^2=N，a>=b>0

1）如果只有一组正整数解，这样的N有哪些，给出所有的N
2）对于确定的N，解有几组。可以给出计数方法吗

wayne 发表于 2012-1-19 10:06:53

{2,5,8,10,13,17,18,20,25,26,29,32,34,37,40,41,45,52,53,58,61,68,72,73,74,80,82,89,90,97,98,100,101,104,106,109,113,116,117,122,128,136,137,146,148,149,153,157,160,162,164,169,173,178,180,181,193,194,197,202,208,212,218,225,226,229,232,233,234,241,242,244,245,257,261,269,272,274,277,281,288,289,292,293,296,298,306,313,314,317,320,328,333,337,346,349,353,356,360,362,369,373,386,388,389,392,394,397,400,401,404,405,409,416,421,424,433,436,449,452,457,458,461,464,466,468,477,482,488,490,509,512,514,521,522,538,541,544,548,549,554,557,562,569,577,584,586,592,593,596,601,605,612,613,617,626,628,634,637,640,641,648,653,656,657,661,666,673,674,676,677,692,698,701,706,709,712,720,722,724,733,738,746,757,761,769,772,773,776,778,788,794,797,801,802,808,809,810,818,821,829,832,833,841,842,848,853,857,866,872,873,877,881,882,898,900,904,909,914,916,922,928,929,932,936,937,941,953,954,964,968,976,977,980,981,997}

wayne 发表于 2012-1-19 10:07:16

谁能给一个分析

hujunhua 发表于 2012-1-19 10:27:35

N=a2p
其中a仅有4m+3型的素因子，p为4m+1型素数

hujunhua 发表于 2012-1-19 10:27:50

N=a2p
其中a仅有4m+3型的素因子，p为4m+1型素数

wayne 发表于 2012-1-19 10:42:44

明白了那么一点意思
多谢老大及时而给力的答复

hujunhua 发表于 2012-1-19 10:47:18

第2个问题，参看你的老帖，第9楼

wayne 发表于 2012-1-19 10:54:01

7# hujunhua
嗯，我记得，
我是在做最近OO发的题才有此疑问的，准确的说，是既熟悉又陌生，
http://projecteuler.net/problem=224
http://bbs.emath.ac.cn/thread-3956-1-1.html

万分感谢！

wayne 发表于 2012-1-19 11:08:04

7# hujunhua

高斯整数
艾森斯坦整数
代数数真是博大精深啊

〇〇 发表于 2012-1-19 12:10:20

2# wayne


怎么算出来的？
页: [1] 2
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