Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772615 | Journal of Number Theory | 2017 | 7 Pages |
Abstract
For a positive integer n and a fixed positive integer q, let Cn=âk=1n(k3+q3). We prove that Cn is not a powerful number if nâ¥maxâ¡{q,1198âq}, using some basic estimates on primes in arithmetic progressions. As applications of our main results, we discuss the powerfulness of Cn for 1â¤qâ¤10.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Chuanze Niu, Wenxin Liu,