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Positive integer couples

Source: Greek MO 2012 - P1

May 12, 2013

parameterizationnumber theory proposednumber theory

Problem Statement

Let positive integers

p,q

with

\gcd(p,q)=1

such as

p+q^2=(n^2+1)p^2+q

. If the parameter

n

is a positive integer, find all possible couples

(p,q)