5

Part of 2022 Moscow Mathematical Olympiad

Problems(1)

Divisibility of special form

Source: Moscow mathematic olympiad 2022, Day 2 P11.5

Tanya wrote numbers in forms

n^7-1

n=2,3,...

and noticed that for

n=8

she got number divisible by

337

. For what minimal

n

did she get number divisible by

2022