Number theory · Diophantine equations · Completing the square · Sums of two squares · Quadratic discriminant
Find all pairs of integers \(m\) and \(n\) satisfying
\[ 2m^{2} + n^{2} = 2mn + 3n . \]
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Serbian Regional Competition (Okruzno takmicenje) 2003, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source