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Divisibility of special form

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

September 29, 2022

number theory

Problem Statement

Tanya wrote numbers in forms

n^7-1

for

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