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a^ab^b has exactly 98 zeros

Source: Austrian - Polish 1998 APMC

May 4, 2020
number theoryDigits

Problem Statement

Consider all pairs (a,b)(a, b) of natural numbers such that the product aabba^ab^b written in decimal system ends with exactly 9898 zeros. Find the pair (a,b)(a, b) for which the product abab is the smallest.
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