On the representation of a number as a sum of the k-th powers in an arithmetic progression

• Published in: Algebra and Discrete Mathematics
• Date: 2003
• Main Author: Prosyanyuk, N.S.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2003
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/155714
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the representation of a number as a sum of the k-th powers in an arithmetic progression / N.S. Prosyanyuk // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 2. — С. 87–92. — Бібліогр.: 8 назв. — англ.

In this paper we obtain the asymptotic formula for a natural n ≤ x which representate as a sum of two non-negative k-th powers in an arithmetic progression.