4

Part of 2018 Grand Duchy of Lithuania

Problems(1)

d - k and d are divisors of n

Source: 2018 Grand Duchy of Lithuania, Mathematical Contest p4 (Baltic Way TST)

Find all positive integers

n

for which there exists a positive integer

k

such that for every positive divisor

d

n

d - k

is also a (not necessarily positive) divisor of

n

number theorydividesdivisor