Number theory · Divisibility · Congruences · Last digits · Quadratic forms
Problem 3, 2005
Let \(x\) and \(y\) be integers such that \(90\) divides \(x^{2} + xy + y^{2}\). Prove that then \(900\) divides \(xy\).
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Serbian Regional Competition 2005, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source