Number theory · Diophantine equations · Quadratic forms · Factorisation · Prime divisors
Find every pair of integers \(x\) and \(y\) satisfying
\[ 2\left(x^2 + y^2\right) = 5\left(xy + 1\right) . \]
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Serbian Regional Competition (Okruzno takmicenje) 1996, high school grade I, problem 1. The 1996 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS). Source