The inequality $0 < x+y \leq 60$ and the equation $17x+29y=1222$. How do you find x and y other than bashing?
Edit: I forgot to mention x and y are integers
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Just find all solutions $(x,y)$ of this linear Diophantine equation. Then add. As a hint, you can start with one solution $(x,y)=1222\cdot (12,-7)$, by the Euclidean algorithm. All solutions arise by adding the ones for the homogeneous equation. – Dietrich Burde Mar 31 '24 at 18:29
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Have you forgotten to mention that x and y must be integers (or perhaps positive integers) – WW1 Mar 31 '24 at 18:34
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@whpowell96 Yes, there is a reason. But even better, the OP confirmed it now. – Dietrich Burde Mar 31 '24 at 18:36