若m,n是整数,且n2+3m2n2=30m2+517,求3m2n2.
问题描述：
若m,n是整数,且n2+3m2n2=30m2+517,求3m2n2.
答
n^2+3m^2n^2=30m^2+517,n^2(1+3m^2)=30m^2+517等式右边为奇数,要等式成立,则等式左边n^2,3m^2+1应均为奇数,n^2为奇数,m^2为偶数.n^2=(30m^2+517)/(3m^2+1)=(30m^2+10+507)/(3m^2+1)=10+507/(3m^2+1)507≥3m^2+1m^2≤...