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Problem 6 of Third round

Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade

September 1, 2019
number theory

Problem Statement

a,b,m,k∈Za,b,m,k\in \mathbb{Z}, a,b,m>2,k>1a,b,m>2,k>1, for which kna+bk^n a+b is an mm-th power of a natural number for ∀n∈N\forall n\in \mathbb{N}. Prove that bb is an mm-th power of a non-negative integer.
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