Correction to: Polynomial values of products of terms from an arithmetic progression

1 Correction to: Monatsh Math https://doi.org/10.1007/s00605-020-01422-7

The constant C in Theorem 2.2 should also depend on the common difference d, however, this dependence is not indicated. We note that from the argument (from the tools used) one can see that C in fact depends also on d, indeed. This error has no influence of any other part of the paper, however, it may be disturbing so it is better be corrected. We are grateful to Yuri Bilu for pointing out this error. Theorem 2.2. correctly should read as

Theorem 2.2

Let $k\ge 8$, $0\le j\le k-1$ and let $a,b\in {\mathbb {Q}}$ with $a\ne 0$. Then for all solutions of the equation

$$\begin{aligned} f_{k,j}(x)=ay^n+b \end{aligned}$$

(4)

in integers x, y, n with $n\ge 2$ we have $\max (|x|,|y|,n)<C$, where C is an effectively computable constant depending only on k, d, a, b. Here we use the convention that for $|y|\le 1$ we have $n=2,3$.