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p is a divisor of 5^m7^n-1

Source: 2021 Dutch IMO TST 3.4

December 28, 2021

number theorydivisor

Problem Statement

Let

p > 10

be prime. Prove that there are positive integers

m

and

n

with

m + n < p

exist for which

p

is a divisor of

5^m7^n-1

.

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