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Minimum value of exponent in diophantine equation with 4 unknowns

Source: Turkey Junior National Olympiad 2022 P3

December 23, 2022
number theoryDiophantine equation

Problem Statement

Let m,n,a,km, n, a, k be positive integers and k>1k>1 such that the equality 5m+63n+49=ak5^m+63n+49=a^k holds. Find the minimum value of kk.
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