The greatest prime divisor of a product of terms in an arithmetic progression
The main result of this paper is the following: Theorem. Let \(d\) and \(k\) be rational integers \({}\geq 3\), then the greatest prime factor of the product \(n(n+d)\cdots (n+(k-1)d)\) is \({}>2k\), except for finitely many (explicitly given) exceptions. The proof is very delicate and contains the study of many subcases. The results used are also numerous and of a great variety.
greatest prime factor products of integers in arithmetic progressions
scientific article; zbMATH DE number 5078186
scientific article