Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Integers with digits 0 or $ 1$


Authors: D. H. Lehmer, K. Mahler and A. J. van der Poorten
Journal: Math. Comp. 46 (1986), 683-689
MSC: Primary 11A63; Secondary 11Y99
MathSciNet review: 829638
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ g \geqslant 2$ be a given integer and $ \mathcal{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 \equiv a\;\pmod k$, $ l \in \mathcal{L}$ and show that such a congruence either has infinitely many solutions, or no solutions in $ \mathcal{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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11A63, 11Y99

Retrieve articles in all journals with MSC: 11A63, 11Y99


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0829638-5
PII: S 0025-5718(1986)0829638-5
Article copyright: © Copyright 1986 American Mathematical Society