Number theory · Decimal digits · Divisibility · Diophantine equations
Find all triples of pairwise distinct nonzero decimal digits \(a\), \(b\), \(c\) for which the fractions
\[ \frac{\overline{ab}}{\overline{bc}} \qquad \text{and} \qquad \frac{a}{c} \]
have the same value. Here \(\overline{ab}\) denotes the two-digit number with tens digit \(a\) and units digit \(b\), and likewise for \(\overline{bc}\).
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Serbian Municipal Competition 2001, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source