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2m-n+13p=2072,\\3m+11n+13p=2961.

Source: Moldova EGMO TST 2023

February 4, 2023
number theoryprime numbersalgebrasystem of equations

Problem Statement

Find all triplets of prime numbers (m,n,p)(m, n, p), that satisfy the system of equations: {2m−n+13p=2072,3m+11n+13p=2961.\left\{\begin{matrix} 2m-n+13p=2072,\\3m+11n+13p=2961.\end{matrix}\right.
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