Abstract. In this paper, we consider the Diophantine equationwhere a, b, c, d, k, l are given integers with gcd(a,We prove that, under some reasonable assumptions, the above equation has only finitely many solutions.

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We investigate polynomial values of sums of products of consecutive integers. For the degree two case we give effective finiteness results, while for the higher degree case we provide ineffective finiteness theorems. For the latter purpose, we also show that the polynomials corresponding to the sums of products we investigate, are indecomposable.