Number theory · Diophantine equations · Prime factorisation · Divisors · Symmetric expressions
Find every triple \((x, y, z)\) of positive integers for which
\[ xyz + xy + xz + yz + x + y + z = 2000 . \]
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Serbian Regional Competition (Okruzno takmicenje) 2001, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source