Problem

Source: Kyiv City MO 2021 Round 1, Problem 8.1

Tags: Fractions, number theory, algebra



Find all positive integers $n$ that can be subtracted from both the numerator and denominator of the fraction $\frac{1234}{6789}$, to get, after the reduction, the fraction of form $\frac{a}{b}$, where $a, b$ are single digit numbers. Proposed by Bogdan Rublov