m,n是整数,n^2+3(m^2)(n^2)=30(m^2)+517,求3(m^2)(n^2)

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m,n是整数,n^2+3(m^2)(n^2)=30(m^2)+517,求3(m^2)(n^2)
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m,n是整数,n^2+3(m^2)(n^2)=30(m^2)+517,求3(m^2)(n^2)
m,n是整数,n^2+3(m^2)(n^2)=30(m^2)+517,求3(m^2)(n^2)

m,n是整数,n^2+3(m^2)(n^2)=30(m^2)+517,求3(m^2)(n^2)
由n^2+3m^2n^2=30m^2+517得
(3m^2+1)(n^2-10)=507=3*13*13
因为m,n都是整数所以3m^2+1,n^2-10都是整数
容易得3m^2+1=13,n^2-10=3*13----------保证m,n是整数
故m^2=4,n^2=49
因此3m^2n^2=3*4*49=588