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five digits 1,4,2,8,6 appear somewhere in decimal expression of a<b

Source: Argentina 2001 OMA L3 p3

May 12, 2024
number theoryDigits

Problem Statement

Let aa and bb be positive integers, a<ba < b, such that in the decimal expansion of the fraction ab\dfrac{a}{b} the five digits 1,4,2,8,61,4,2,8,6 appear somewhere, in that order and consecutively. Determine the lowest possible value bb can take .
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