Pigeonholes and Repunits

It is well known that any integer k has a multiple consisting of only the digits 1's and 0's. As an extension of this result, we study integers of the form 111 ... 000 or 111 ... 111 that is a multiple of k. We show that if k > 2 and k is not a power of 3, then the multiple can be chosen to have at most k - 1 digits.

By: Chai Wah Wu

Published in: American Mathematical Monthly, volume 121, (no 6), pages 529-533; 10.4169/amer.math.monthly.121.06.529 in 2014

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