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4^x + 4^y + 4^z = u^2

Source: 1991 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p1

November 20, 2022

number theoryPerfect SquaresDiophantine equationdiophantine

Problem Statement

Determine all solutions of the equation

4^x + 4^y + 4^z = u^2

for integers

x,y,z

and

u