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Cubes in {0,1,...,n}3

Eugen J. Ionascu / Rodrigo A. Obando
Published Online: 2012-11-30 | DOI: https://doi.org/10.1515/integers-2012-0039


The main aim of this paper is to describe a procedure for calculating the number of cubes that have coordinates in the set {0,1,...,n}. For this purpose we continue and, at the same time, revise some of the work begun in a sequence of papers about equilateral triangles and regular tetrahedra all having integer coordinates for their vertices. We adapt the code that was included in a paper by the first author and was used to calculate the number of regular tetrahedra with vertices in {0,1,...,n}3. The idea is based on the theoretical results obtained by the first author with A. Markov. We then extend the sequence A098928 in the Online Encyclopedia of Integer Sequences to the first one hundred terms.

Keywords: Diophantine Equations; Integers

About the article

Received: 2010-12-20

Revised: 2011-02-27

Accepted: 2011-04-09

Published Online: 2012-11-30

Published in Print: 2012-12-01

Citation Information: Integers, Volume 12, Issue 6, Pages 1247–1263, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2012-0039.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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