MathDB

14

Part of 1997 IMO Shortlist

Problems(1)

Same divisor

Source: IMO Shortlist 1997, Q14, China TST 2005

3/6/2004
Let b,m,n b, m, n be positive integers such that b>1 b > 1 and m≠n. 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.
number theoryprime divisorsprime numbersDivisibilityIMO Shortlistpower of 2Zsigmondy