TY - JOUR

T1 - Integers with digits 0 or 1

AU - Lehmer, D. H.

AU - Mahler, K.

AU - Van Der Poorten, A. J.

PY - 1986

Y1 - 1986

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84915948138&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-1986-0829638-5

DO - 10.1090/S0025-5718-1986-0829638-5

M3 - Article

VL - 46

SP - 683

EP - 689

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 174

ER -