4

Part of 2020 German National Olympiad

Problems(1)

Finding all integers with a divisibility condition

Source: Germany 2020, Problem 4

Determine all positive integers

n

for which there exists a positive integer

d

with the property that

n

is divisible by

d

n^2+d^2

is divisible by

d^2n+1

number theorynumber theory proposedDivisibilityDivisors