MathDB

N3

Part of 2015 Indonesia MO Shortlist

Problems(1)

Divisibility of power of integer

Source:

10/23/2017
Given positive integers a,b,c,da,b,c,d such that a∣cda\mid c^d and b∣dcb\mid d^c. Prove that ab∣(cd)max(a,b) ab\mid (cd)^{max(a,b)}
Divisibilitynumber theory