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multiple of k <= k^4 whose decimal expension has at most 4 distinct digits

Source: 1995 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p4

January 27, 2020
multipleDigitsnumber theory

Problem Statement

Prove that every integer k>1k > 1 has a multiple less than k4k^4 whose decimal expension has at most four distinct digits.