Number theory · Diophantine equations · Quadratic residues · Parity · Infinite descent
Problem 3, 2005
Determine all triples of integers \((x, y, z)\) that satisfy
\[ x^{2} + y^{2} + z^{2} = 2004\,xyz . \]
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Serbian Municipal Competition 2005, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source