MathDB
Truly peculiar NT

Source: EGMO 2024 P3

April 13, 2024
number theorygreatest common divisorEGMO

Problem Statement

We call a positive integer nn{} peculiar if, for any positive divisor dd{} of nn{} the integer d(d+1)d(d + 1) divides n(n+1).n(n + 1). Prove that for any four different peculiar positive integers A,B,CA, B, C and DD{} the following holds: gcd(A,B,C,D)=1.\gcd(A, B, C, D) = 1.