5

Part of 2021 Dutch Mathematical Olympiad

Problems(1)

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

Source: Dutch NMO 2021 p5

We consider an integer

n > 1

with the following property: for every positive divisor

d

n

d + 1

is a divisor of

n + 1

n

is a prime number.

number theoryprimedivisor