MathDB

n is prime if for every divisor d of n, d + 1 is a divisor of n + 1

Source: Dutch NMO 2021 p5

December 28, 2021

number theoryprimedivisor

Problem Statement

We consider an integer

n > 1

with the following property: for every positive divisor

d

n

we have that

d + 1

is a divisor of

n + 1

. Prove that

n

is a prime number.