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IMO Shortlist 2012, Number Theory 6

Source: IMO Shortlist 2012, Number Theory 6

July 26, 2013

modular arithmeticnumber theoryDivisibilityIMO Shortlist

Problem Statement

Let

x

and

y

be positive integers. If

{x^{2^n}}-1

is divisible by

2^ny+1

for every positive integer

n

, prove that

x=1