Number theory · Diophantine equations · Quadratic forms · Factorisation · Quadratic discriminant · Parametrisation
Let \(m\) be an arbitrary integer. Prove that there is at least one pair \((x, y)\) of integers for which
\[ 2x^2 + 11xy + 12y^2 + 4x + 5y + 6 = 2m . \]
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Serbian Republic Competition (Republicko takmicenje) 1999, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source