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Find the solutions of p=m^2+n^2, p|m^3+n^3-4

Source: Iranian National Olympiad (3rd Round) 2004

January 9, 2009
number theory proposednumber theory

Problem Statement

Find all prime numbers pp such that p=m2+n2 p = m^2 + n^2 and p∣m3+n3−4p\mid m^3+n^3-4.
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