Number theory · Rational solutions · Reduced fractions · Divisibility · Diophantine equations · Rational root theorem
Find all rational numbers \(r\) and all integers \(k\) that satisfy
\[ r\bigl(5k - 7r\bigr) = 3 . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2009, 1. letnik, category A, problem 4. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source