Difference between revisions of "Talk:1988 IMO Problems/Problem 6"

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-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 :)

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