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Multiples of M have the same digital sum

Source: Kürschák 1989, problem 2

July 20, 2014
number theory unsolvednumber theory

Problem Statement

For any positive integer nn denote S(n)S(n) the digital sum of nn when represented in the decimal system. Find every positive integer MM for which S(Mk)=S(M)S(Mk)=S(M) holds for all integers 1≤k≤M1\le k\le M.
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