MathDB

Same divisor

Source: IMO Shortlist 1997, Q14, China TST 2005

March 6, 2004

number theoryprime divisorsprime numbersDivisibilityIMO Shortlistpower of 2Zsigmondy

Problem Statement

Let

b, m, n

be positive integers such that

b > 1

and

m \neq n.

Prove that if b^m \minus{} 1 and b^n \minus{} 1 have the same prime divisors, then b \plus{} 1 is a power of 2.