On the product of consecutive elements of an arithmetic progression (Q1068877)

\textit{P. Erdős} and \textit{J. L. Selfridge} [Ill. J. Math. 19, 292-301 (1975; Zbl 0295.10017)] proved that the product of \(k\geq 2\) consecutive integers cannot be a proper power and asked for an analogous result concerning the product of consecutive integers of an arithmetic progression. Using the method of the above-mentioned paper, the author proves that the product \((n+d)(n+2d)\cdot \cdot \cdot (n+kd)\) cannot be a proper power provided k is sufficiently large; in fact, for all cases, the largest k is \[ \leq \quad \max \{3\cdot 10^ 4, (3/2) \exp [d(d+2)(d+1)^{1/3}]\}. \]