International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 1, Pages 77-80

On the representation of m as k=nnϵkk

Lane Clark

Department of Mathematics, Southern Illinois University at Carbondale, Carbondale 62901-4408, IL, USA

Received 3 September 1998

Copyright © 2000 Lane Clark. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let A(n,m) be the number of solutions of k=nnϵkk=m where each ϵk{0,1}. We determine the asymptotic behavior of A(n,m) for m=o(n3/2), extending results of van Lint and of Entringer.