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Distinct prime numbers

Source: Bosnia and Herzegovina TST 2010 problem 1

March 30, 2014
number theoryprime numbersnumber theory proposed

Problem Statement

a)a) Let pp and qq be distinct prime numbers such that p+q2p+q^2 divides p2+qp^2+q. Prove that p+q2p+q^2 divides pqāˆ’1pq-1. b)b) Find all prime numbers pp such that p+121p+121 divides p2+11p^2+11.
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