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Let a be a positive integer. We study the Diophantine equation n ∏ k=1 (ak + (2a− a)k + 1) = y. This Diophantine equation generalizes a result of Gürel [5] for a = 2. We also prove that the product (2 − 1)(3 − 1) . . . (n − 1) is a perfect square only for the values n for which the triangular number Tn is a perfect square.

On products of quartic polynomials over consecutive indices which are perfect squares