6

Part of 2019 Regional Olympiad of Mexico Center Zone

Problems(1)

A problem with perfect powers

Source: P6, Mexico Center Regional Olympiad 2019

Find all positive integers

m

with the next property: If

d

is a positive integer less or equal to

m

and it isn't coprime to

m

, then there exist positive integers

a_{1}, a_{2}

a_{2019}

(where all of them are coprimes to

m

m+a_{1}d+a_{2}d^{2}+\cdot \cdot \cdot+a_{2019}d^{2019}

is a perfect power.