Integers with digits 0 or

Authors:
D. H. Lehmer, K. Mahler and A. J. van der Poorten

Journal:
Math. Comp. **46** (1986), 683-689

MSC:
Primary 11A63; Secondary 11Y99

DOI:
https://doi.org/10.1090/S0025-5718-1986-0829638-5

MathSciNet review:
829638

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Abstract: Let be a given integer and the set of nonnegative integers which may be expressed in base *g* employing only the digits 0 or 1. Given an integer , we study congruences , and show that such a congruence either has infinitely many solutions, or no solutions in . 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.

**[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.

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0829638-5

Article copyright:
© Copyright 1986
American Mathematical Society