Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A new variant of the Hilbert-Waring problem


Authors: Tianxin Cai and Deyi Chen
Journal: Math. Comp. 82 (2013), 2333-2341
MSC (2010): Primary 11P05; Secondary 11D85, 11D72
Published electronically: March 5, 2013
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we propose a new variant of Waring's problem: to express a positive integer $ n$ as a sum of $ s$ positive integers whose product is a $ k$-th power. We define, in a similar way to that done for $ g(k)$ and $ G(k)$ in Waring's problem, numbers $ g'(k)$ and $ G'(k)$. We obtain $ g'(k)=2k-1$, $ G'(p)\leq p+1$ for primes $ p$, $ G'(2p)\leq 2p+2$ for odd primes $ p$. Moreover, we obtain several interesting results and make two conjectures about $ G'(3)$ and $ G'(4)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 11P05, 11D85, 11D72

Retrieve articles in all journals with MSC (2010): 11P05, 11D85, 11D72


Additional Information

Tianxin Cai
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, 310027, China
Email: txcai@zju.edu.cn

Deyi Chen
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, 310027, China
Email: chendeyi1986@126.com

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02685-3
PII: S 0025-5718(2013)02685-3
Received by editor(s): September 4, 2011
Received by editor(s) in revised form: January 22, 2012, January 27, 2012, and February 1, 2012
Published electronically: March 5, 2013
Additional Notes: Project supported by China National Science Foundation Grant No.10871169.
Article copyright: © Copyright 2013 American Mathematical Society