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Diophantine equation at romanian tst

Source: Romanian IMO TST 2006, day 4, problem 2

May 19, 2006
quadraticsreal analysiscomplex numbersalgebrapolynomialsum of rootsnumber theory proposed

Problem Statement

Find all non-negative integers m,n,p,qm,n,p,q such that pmqn=(p+q)2+1. p^mq^n = (p+q)^2 +1 .
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