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
AN - SCOPUS:84915948138
SN - 0025-5718
VL - 46
SP - 683
EP - 689
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 174
ER -