Number theory · Diophantine equations · Rational points · Quadratic residues · Coprimality
How many pairs \((x, y)\) of rational numbers satisfy \(2x^{2} + 5y^{2} = 1\)?
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Serbian Regional Competition (Okruzno takmicenje) 1999, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source