由 ---- 於 星期二 五月 27, 2003 4:55 pm
I can never solve your second question, meowth, but for the first question,
3M^2+2N^2=35
If M=0(mod 3)
3M^2<35
M=3
3M^2=0(mod 27)
35=8(mod 27)
So 2N^2=8(mod 27)
N^2=4(mod 27)
2N^2<35
So N^2=4
N= (+/-)2
When M=3k(+/-)1,
3M^2=3(mod 9)
35=8(mod 9)
So 2N^2=5(mod 9)
Since 2N^2<35
2N^2=5, 14, 23, 32
N^2=16 (5/2, 7, 23/2 rejected)
N=(+/-)4