Powerful numbers in the product of consecutive integer values of a polynomial
Article Type
Research Article
Publication Title
Publicationes Mathematicae
Abstract
Let n and r be positive integers. Also let k be an odd positive integer and d be a non-negative integer. In this paper, we prove that if k has at most four distinct prime factors, then the product ((d + 1)k + rk)((d + 2)k + rk) · · · ((d + n)k + rk) is not a powerful number for n ≥ max{r+d, 59−r−d}. As a consequence, we prove that if k has at most four distinct prime factors, then the product (1k + 1)(2k + 1) · · · (nk + 1) is not a powerful number.
First Page
319
Last Page
336
DOI
10.5486/PMD.2019.8272
Publication Date
1-1-2019
Recommended Citation
Dey, Pallab Kanti and Laishram, Shanta, "Powerful numbers in the product of consecutive integer values of a polynomial" (2019). Journal Articles. 1030.
https://digitalcommons.isical.ac.in/journal-articles/1030