Euler was unable to solve the problem, but in this work he demonstrated methods for constructing Graeco-Latin squares where is odd or a multiple of 4. Observing that no order two square exists and being unable to construct an order six square, he conjectured that none exist for any oddly even number The non-existence of order six squares was confirmed in 1901 by Gaston Tarry through a proof by exhaustion. However, Euler's conjecture resisted solution until the late 1950s, but the problem has led to important work in combinatorics.