Question

若m、n是整数,且n²+3m²n²=30m²+517,则3m²n

Answer 1

n²+3m²n²=30m²+517

n^2+3m^2n^2-30m^2=517

n^2+3m^2(n^2-10)=517

n^2-10+3m^2(n^2-10)=517-10

(3m^2+1)(n^2-10)=507=3*13*13

n^2-10=39,3m^2+1=13

n^2=49,m^2=4

3m²n²=3*4*49=588