Powers from products of terms in progressions with gaps
Volume 210 / 2023
Acta Arithmetica 210 (2023), 205-222
MSC: Primary 11D41; Secondary 11G05.
DOI: 10.4064/aa220811-13-9
Published online: 26 October 2023
Abstract
We find all perfect $\ell $th powers that may be expressed as a product of $k-1$ terms from a nontrivial coprime $k$-term arithmetic progression, for $5 \leq k \leq 8$ and $\ell \geq 3$ prime. The result depends upon machinery from the so-called Modular Method, with some additional and crucial use of local information. This sharpens earlier work of Das, Laishram and Saradha [Int. J. Number Theory 19 (2023), 1707–1744].
