Talk:1988 IMO Problems/Problem 6

I just wonder if it's possible to solve this problem with Chinese Remainder Theorem

First: assuming that GCD(a,b)=1.

Then quotient is always square mod a and mod b and is less or equal than a times b and is not divisible by neither a nor b which implies it's square of integer.

In case of GCD(a,b) = d>1 we can transform quotient to d^2((a_1)^2 + (b_1)^2)/(d^2*a_1*b_1 + 1) where a_1 = a/d and b_1 = b/d and follow the same reasoning as above.

It's just an idea without final and rigorous proof.

Am I mistaken?

Help :)