Integers with digits 0 or 1

D. H. Lehmer*, K. Mahler, A. J. Van Der Poorten

*Corresponding author for this work

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Abstract

Let g > 2 be a given integer and L the set of nonnegative integers which may be expressed in base g employing only the digits 0 or 1. Given an integer k > 1, we study congruences l = a (mod/c), lϵL and show that such a congruence either has infinitely many solutions, or no solutions in L. There is a simple criterion to distinguish the two cases. The casual reader will be intrigued by our subsequent discussion of techniques for obtaining the smallest nontrivial solution of the cited congruence.

Original languageEnglish
Pages (from-to)683-689
Number of pages7
JournalMathematics of Computation
Volume46
Issue number174
DOIs
Publication statusPublished - 1986

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Lehmer, D. H., Mahler, K., & Van Der Poorten, A. J. (1986). Integers with digits 0 or 1. Mathematics of Computation, 46(174), 683-689. https://doi.org/10.1090/S0025-5718-1986-0829638-5