1984 IMO Problems/Problem 2
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Find one pair of positive integers such that is not divisible by , but is divisible by .
So we want and , so we want . Now take e.g. and get . Now by some standard methods like Hensels Lemma (used to the polynomial , so seen as constant from now) we get also some with and , so and we are done. (in this case it gives )
This solution was posted and copyrighted by ZetaX. The original thread for this problem can be found here: 
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