2004 Pan African MO Problems/Problem 1
Do there exist positive integers and such that:
Note that can only be congruent to modulo 9. So we can check the remainder when is divided by 9. There are only nine cases to check, so we can do it manually. To make computation easier, we can factor the left-hand side as .
There are no cases of where or , so there are no positive integers that satisfies the original equation.
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