Find the smallest positive integer N with the following property: of the three numbers N, N+1, and N+2, one of them is divisible by 2^2,one of them is divisible by 3^2, one is divisible by 5^2,and one is divisible by 7^2.

Not sure if I understand your question! But:

If N = 98 mod 7^2 =0

N =98+1 = 99 mod 3^2 =0

N =99 + 1 = 100 mod 2^2 =0 and mod 5^2 =0

Does that make sense ???.