Re: [代數] 清大數學一題
※ 引述《luke2 (路克：２)》之銘言：
: 還有一題，我覺得無解＝ ＝
: 不過我是用列舉的就是了
: p,q為正整數,且
: p^2+3q^2 =11907
: p^2+3q^2=3^5*7^2
: p^2=3(63+q)(63-q)
: 求p與q的植
: 很明顯q要是3的倍數
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
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