On products of disjoint blocks of arithmetic progressions and related equations

TL;DR

This paper investigates Diophantine equations involving products of disjoint blocks of arithmetic progressions, inspired by Erdős and Graham's question, aiming to understand their solutions and properties.

Contribution

It introduces new results on the solutions of equations involving products of disjoint arithmetic progression blocks, expanding the understanding of such Diophantine problems.

Findings

Identified conditions for solutions to specific product equations

Extended previous results on products of consecutive integers

Provided new bounds and classifications for solutions

Abstract

In this paper we deal with Diophantine equations involving products of consecutive integers, inspired by a question of Erd\H{o}s and Graham.