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simplify fraction (V Soros Olympiad 1998-99 Round 2 9.4)

Source:

May 25, 2024
algebranumber theory

Problem Statement

Simplify the fraction 123456788...876543211234567899...987654321\frac{123456788...87654321}{1234567899...987654321}’ if the digit 88 in the numerator occurs 20002000 times, and the digit 99 in the denominator 19991999 occurs times (as a result you need to get an irreducible fraction).
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