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x^2 + y^2 + p^z = 2003 diophantine

Source: Singapore Open Math Olympiad 2003 2nd Round p3 SMO

April 2, 2020
diophantineDiophantine equationnumber theory

Problem Statement

For any given prime pp, determine whether the equation x2+y2+pz=2003x^2 + y^2 + p^z = 2003 always has integer solutions in x,y,zx, y, z. Justify your answer
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