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Power and divisibility

Source: Indonesia Mathematics Olympiad 2008 Day 2 Problem 1

August 13, 2008
number theory proposednumber theory

Problem Statement

Let m,n>1 m,n > 1 are integers which satisfy n|4^m \minus{} 1 and 2^m|n \minus{} 1. Is it a must that n \equal{} 2^{m} \plus{} 1?
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