Number theory · Diophantine equations · Sums of three squares · Quadratic residues · Modular arithmetic
Find every triple of integers \(x, y, z\) with
\[ 3x^2 + 3y^2 + 3z^2 + 2x + 2y + 2z = 2004 . \]
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Serbian Republic Competition (Republicko takmicenje) 2006, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source