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k + a^k = m + 2a^m, diophantine in Z+

Source: Czech-Polish-Slovak Junior Match 2012, Team p5 CPSJ

March 12, 2020
Diophantine equationdiophantinenumber theory

Problem Statement

Find all triplets (a,k,m)(a, k, m) of positive integers that satisfy the equation k+ak=m+2amk + a^k = m + 2a^m.
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