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Prove that the number is compound

Source: KJMO 2010 Problem 6

September 6, 2018

number theory

Problem Statement

Let

n\in\mathbb{N}

and

p

is the odd prime number. Define the sequence

a_n

such that

a_1=pn+1

and

a_{k+1}=na_k+1

for all

k \in \mathbb{N}

. Prove that

a_{p-1}

is compound number.

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