27

Part of 1989 IMO Shortlist

Problems(1)

2^{1989} divides m^n - 1

Source: IMO Shortlist 1989, Problem 27, ILL 86

m

be a positive odd integer,

m > 2.

Find the smallest positive integer

n

2^{1989}

divides m^n \minus{} 1.

modular arithmeticnumber theoryleast common multipleDivisibilityIMO Shortlist