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x^2 + y^2 = z^n diophantine

Source: Netherlands - Dutch NMO 1969 p2

January 31, 2023
number theorydiophantineDiophantine equation

Problem Statement

Prove that for all n∈Nn \in N, x2+y2=znx^2 + y^2 = z^n has solutions with x,y,z∈Nx,y,z \in N.
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