Euler proved that the product of four positive integers in arithmeticprogression is not a square. Gyory, using a result of Darmon and Merel, showed that theproduct of three coprime positive integers in arithmetic progression cannot be an l-thpower for l≥ 3. There is an extensive literature on longer arithmetic progressions suchthat the product of the terms is an (almost) power. In this paper we extend the rangeof k's such that the product of k coprime integers in arithmetic progression cannot be acube when 2 < k < 39. We prove a similar result for almost cubes.
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