MathDB

N1

Part of 2017 Pan-African Shortlist

Problems(1)

A 28

Source:

5/25/2007
Prove that the expression gcd⁡(m,n)n(nm)\frac{\gcd(m, n)}{n}{n \choose m} is an integer for all pairs of positive integers (m,n)(m, n) with n≥m≥1n \ge m \ge 1.
number theorygreatest common divisorfloor functionfunctionalgebraDivisibility Theory