作者perceval (摸鱼中)
看板Math
标题Re: [代数] 清大数学一题
时间Tue Apr 12 04:28:57 2011
※ 引述《luke2 (路克：２)》之铭言：
: 还有一题，我觉得无解＝ ＝
: 不过我是用列举的就是了
: p,q为正整数,且
: p^2+3q^2 =11907
: p^2+3q^2=3^5*7^2
: p^2=3(63+q)(63-q)
: 求p与q的植
: 很明显q要是3的倍数
3 | 11907 => 3| p^2+3q^2 => 3|p^2 => 3|p
3^2 | 11907 => 3^2| p^2+3q^2 => 3|q^2 => 3|q
....
3^2|q, 3^3|p
Let p=3^3 r, q=3^2 s
=> 3 r^2 +s^2= 7^2=49
Try r =1,2,3,4 => r=4,s=1 => p=108, q=9
--
The whole problem with the world is that fools and fanatics are
always so certain of themselves, but wiser people so full of doubts.
– Bertrand Russell
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 140.116.250.190
1F：→ luke2 :我当初也是一直提, 不过算不出来,唉 04/12 06:13
2F：→ luke2 :谢谢!! 04/12 06:13