MathDB

Brazil 1995

Source: Brazilian olympiad, 1995, Day one, Problem 3

December 4, 2003

greatest common divisornumber theoryprime divisorinequalities

Problem Statement

For any positive integer

n>1

, let

P\left(n\right)

denote the largest prime divisor of

n

. Prove that there exist infinitely many positive integers

n

for which P\left(n\right)