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 $7^2$.
The smallest number that works is 1223 (1224 is divisible by 4 and 9, 1225 is divisible by 25 and 49).
The smallest positive n =98, 98+1, 98+2=98, 99,100
100 mod 2^2 =0
100 mod 5^2 =0
99 mod 3^2 =0
98 mod 7^2 =0
+83 
