Resumen de Cubes in products of terms in arithmetic progression

Lajos Hajdu, Szabolcs Tengely, Robert Tijdeman

• Euler proved that the product of four positive integers in arithmetic progression is not a square. Gy}ory, using a result of Darmon and Merel, showed that the product of three coprime positive integers in arithmetic progression cannot be an l-th power for l ¸ 3. There is an extensive literature on longer arithmetic progressions such that the product of the terms is an (almost) power. In this paper we extend the range of k's such that the product of k coprime integers in arithmetic progression cannot be a cube when 2 < k < 39. We prove a similar result for almost cubes.