# Euler square

An Euler square is a square array made by combining *n* objects of two types such that
the first and second elements form a Latin
square. Euler squares are also known as **Graeco-Latin squares**, **Graeco-Roman squares**, or **Latin-Graeco squares**.
For many years, Euler squares were known to exist for *n* = 3, 4,
and for every odd *n* except *n* = 3*k*. Euler's **Graeco-Roman squares conjecture** maintained that there are
no Euler squares of order *n* = 4*k* + 2 for *k* =
1, 2, .... However, such squares were found to exist in 1959 by Bose and
Shrikande, refuting the conjecture.