Lehmer, D. H.; Mahler, K.; van der Poorten, A. J. Integers with digits 0 or 1. (English) Zbl 0589.10004 Math. Comput. 46, 683-689 (1986). The authors study congruences \(\ell \equiv a (mod k)\), \(k>1\) an integer and show that such a congruence has either infinitely many solutions \(\ell\) or no solution \(\ell\), where \(\ell\) shall be a nonnegative integer which may be expressed in base g (g fixed) using only the digits 0 or 1. Techniques that allow to obtain the smallest nontrivial solution are discussed. Reviewer: P.Kirschenhofer Cited in 2 Documents MSC: 11A63 Radix representation; digital problems 11A07 Congruences; primitive roots; residue systems Keywords:g-adic representation; digital properties; congruences PDFBibTeX XMLCite \textit{D. H. Lehmer} et al., Math. Comput. 46, 683--689 (1986; Zbl 0589.10004) Full Text: DOI