On the representation of m as ∑k=−nnϵkk

Clark, Lane

doi:https://doi.org/10.1155/S0161171200001885

International Journal of Mathematics and Mathematical Sciences

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Volume 23 |Article ID 836138 | https://doi.org/10.1155/S0161171200001885

Lane Clark, "On the representation of m as ∑k=−nnϵkk", International Journal of Mathematics and Mathematical Sciences, vol. 23, Article ID 836138, 4 pages, 2000. https://doi.org/10.1155/S0161171200001885

On the representation of m as ∑k=−nnϵkk

Lane Clark¹

¹Department of Mathematics, Southern Illinois University at Carbondale, USA

Received03 Sep 1998

Abstract

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.

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Copyright © 2000 Hindawi Publishing Corporation. 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.

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