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Simple division trick

Source: Kyiv City MO 2021 Round 1, Problem 8.1

December 21, 2023
Fractionsnumber theoryalgebra

Problem Statement

Find all positive integers nn that can be subtracted from both the numerator and denominator of the fraction 12346789\frac{1234}{6789}, to get, after the reduction, the fraction of form ab\frac{a}{b}, where a,ba, b are single digit numbers.
Proposed by Bogdan Rublov
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