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a+p and a^2+p^2

Source: Mexico Regional Math Olympiad 2009 Problem 2

September 6, 2015
number theoryprime numbers

Problem Statement

Let p≥2p \ge 2 be a prime number and a≥1a \ge 1 a positive integer with p≠ap \neq a. Find all pairs (a,p)(a,p) such that: a+p∣a2+p2a+p \mid a^2+p^2
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