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Multiple of power of two.

Source: Bulgarian TST, 2020, p2

August 4, 2020
algebranumber theoryTSTBulgaria

Problem Statement

Given two odd natural numbers a,b a,b prove that for each n∈N n\in\mathbb{N} there exists m∈N m\in\mathbb{N} such that either amb2−1 a^mb^2-1 or bma2−1 b^ma^2-1 is multiple of 2n. 2^n.
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