MathDB
Multiple of 2^n has only digits a and b

Source: Baltic Way 1998

January 11, 2011
modular arithmeticinductionnumber theory proposednumber theory

Problem Statement

Let aa be an odd digit and bb an even digit. Prove that for every positive integer nn there exists a positive integer, divisible by 2n2^n, whose decimal representation contains no digits other than aa and bb.
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