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2^{1989} divides m^n - 1

Source: IMO Shortlist 1989, Problem 27, ILL 86

September 18, 2008

modular arithmeticnumber theoryleast common multipleDivisibilityIMO Shortlist

Problem Statement

Let

m

be a positive odd integer,

m > 2.

Find the smallest positive integer

n

such that

2^{1989}

divides m^n \minus{} 1.