Question

一个自然数减去30或者加上31都仍是完全平方数,这个数是几?

Answer 1

A-30 = m^2

A+31 = n^2

n^2-m^2 = 61

(n+m)(n-m) = 1

n+m = 61,n-m=1

n=31,m=30

A = 30+m^2 = 30+30^2 = 930

这个数是930