Number theory · Greatest common divisor · Coprimality · Irreducible fractions · Euclidean algorithm
Find all natural numbers \(n\) for which the fraction
\[ \frac{2n+3}{5n+7} \]
can be reduced, that is, for which its numerator and denominator have a common divisor greater than \(1\).
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Serbian Regional Competition (Okruzno takmicenje) 1996, high school grade I, problem 3. The 1996 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS). Source