P3

Part of 2023 Romania Team Selection Test

Problems(1)

Divisibility with a quadratic and a factorial

Source: Romania TST 2023 Day 2 P3

Given a positive integer

a,

n!

is divisible by

n^2 + n + a

for infinitely many positive integers

n.{}

Proposed by Andrei Bâra

number theoryfactorialDivisibility