Number theory · Diophantine equations · Bounding · Parity
Let \(x\), \(y\) and \(z\) be positive integers satisfying both
\[ x^{3} - y^{3} - z^{3} = 3xyz \qquad \text{and} \qquad x^{2} = 2(y + z). \]
Determine the value of \(x + y + z\).
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Serbian Regional Competition 2010, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source