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Solutions of p^3=p^2+q^2+r^2 in primes

Source: Iranian National Olympiad (3rd Round) 2004

January 9, 2009
Eulernumber theory proposednumber theory

Problem Statement

Find all integer solutions of p^3\equal{}p^2\plus{}q^2\plus{}r^2 where p,q,r p,q,r are primes.