| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4593968 | Journal of Number Theory | 2013 | 5 Pages |
Abstract
In this note, we prove that (i) for any odd prime power ℓ and any positive integer n , the product (1ℓ+1)(2ℓ+1)⋯(nℓ+1)(1ℓ+1)(2ℓ+1)⋯(nℓ+1) is not a powerful number; (ii) for any positive odd number ℓ , there exists an integer NℓNℓ such that for any positive integer n⩾Nℓn⩾Nℓ, the product (1ℓ+1)(2ℓ+1)⋯(nℓ+1)(1ℓ+1)(2ℓ+1)⋯(nℓ+1) is not a powerful number.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yong-Gao Chen, Ming-Liang Gong, Xiao-Zhi Ren,