#### Document Type

Article

#### Publication Date

2008

#### Publication Title

Integers

#### Abstract

This paper is a continuation of the work started by the second author in a series of papers. We extend to the general case the characterization previously found for those equilateral triangles in R3 whose vertices have integer coordinates. In this earlier work, we made use of the hypothesis that (a, b, c) is a non-degenerate primitive solution of a2 +b2 +c2 = 3d2. This condition is now eliminated. Although degenerate solutions present less interest as a result, we state a conjecture which gives a characterization for the existence of such solutions. An approximate extrapolation formula for the sequence ET(n) of all equilateral triangles with vertices in {0, 1, 2, ..., n}3 is given and the asymptotic behavior of this sequence is analyzed.

#### Recommended Citation

Ionascu, Eugen J., "A characterization of all equilateral triangles in Z³" (2008). *Faculty Bibliography*. 162.

http://csuepress.columbusstate.edu/bibliography_faculty/162