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positive integer divisible by 2020 with equal numbers of digits 0, 1, 2,...,9

Source: Tournament of Towns, Junior A-Level Paper, Spring 2020 , p1

June 10, 2020
Digitsnumber theorydivisible

Problem Statement

Does there exist a positive integer that is divisible by 20202020 and has equal numbers of digits 0,1,2,...,90, 1, 2, . . . , 9 ?
Mikhail Evdokimov
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