2017 USAJMO Problems/Problem 1
Prove that there are infinitely many distinct pairs of relatively prime integers and such that is divisible by .
Let and . We see that . Therefore, we have , as desired.
(Credits to laegolas)
Let be any odd number above 1. We have Since is even, This means that and since x is odd, or This means for any odd x, the ordered triple satisfies the condition. Since there are infinitely many values of possible, there are infinitely many ordered triples, as desired.
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