Integer Cevians - Equilateral Triangles

[danieldf]

Is anybody familiar with any theory of integer cevians on equilateral triangles?

More specificaly, I was trying to find something about the number of integer cevians that divide the side in integer parts. Like, the eq triangle of side 8 have cevian 7 dividing one side into 3+5.

Only reference I found is here https://oeis.org/A089025
Where it examples the triangle of side 280 having cevians "247 partitioning an edge into 93+187, as well as cevian 271 that sections the edge into 19+261."
But nothing else online on how to get to these partitions or how many one could find for a specific triangle.

 

[bahamagreen]

INTEGER TRIANGLES WITH INTEGER MEDIANS (5 pages, may be what you are looking for)
http://upet.ro/simpro/2014/proceedings/07 - MATHEMATICS, PHYSICS, INFORMATICS/7.1.pdf

On Triangles with rational altitudes, angle bisectors or medians (108 pages, comprehensive)
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.23.2605&rep=rep1&type=pdf

 

[selfdeception]

Here is a repo with these equilateral triangles and their Cevians with all such instances going up to 7^4:

https://github.com/jprus/eisenstein-triples

It includes the complementary orthogonal Cevian multiplied by sqrt(3). In both cases you have the integer length of the sides of the equilateral triangle as well as the lengths of the partitioned sides all matched to a particular cevian of form "6i+1 prime" (as well as composite numbers with all factors of this form). The information is presented as an array of objects/structs in Racket (ie. modern DrScheme, a language popular in academia and functional programming), JavaScript, and Java so you can continue to experiment with these.