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.
(Credits to kingofgeedorah, 2016 MATHCOUNTS Champion)
|2017 USAJMO (Problems • Resources)|
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