Number theory · Prime factorisation · Divisibility · Bounding
Do there exist positive integers \(a\), \(b\), \(c\) such that
\[ 2010 = (a + b) \cdot (b + c) \cdot (c + a) \, ? \]
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Serbian Regional Competition 2011, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source