On Latin Triangles

Halberstam, Hoffman and Richter introduced the idea of a Latin triangle as an analogue of a Latin square, showed the existence or non-existence of Latin triangles for small orders, and used a multiplication technique to generate triangles of orders \(3^n\) and \(3^n – 1\). We generalize this multiplication theorem and provide a construction of Latin triangles of odd order \(n\) for \(n\) such that \(n+2\) is prime. We also discuss scalar multiplication, orthogonal triangles, and results of computer searches.