Remote Access Mathematics of Computation
Green Open Access

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?)

  • [1] F. M. Dekking, M. Mendes France & A. J. van der Poorten, "FOLDS!," Math. Intelligencer, v. 4, 1982, pp. 130-138; II: pp. 173-181, III: pp. 190-195. MR 684028 (84f:10016a)
  • [2] K. Mahler, Über die Taylorcoeffizienten rationaler Funktionen, Akad. Amsterdam, vol. 38, 1935, pp. 51-60.
  • [3] G. Pólya & G. Szegö, Problems and Theorems in Analysis II (translation of 4th edition 1971), Springer-Verlag, Berlin and New York, 1976, see pp. 34ff.

Similar Articles

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

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

Additional Information

Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society