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A PAIR OF EQUATIONS IN EIGHT PRIME CUBES AND POWERS OF 2

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  14 December 2022

XUE HAN  and
HUAFENG LIU
XUE HAN
Affiliation:
School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, Shandong, PR China e-mail: han_xue@stu.sdnu.edu.cn
HUAFENG LIU*
Affiliation:
School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, Shandong, PR China
*
e-mail: hfliu_sdu@hotmail.com
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Abstract

In this paper, we show that every pair of sufficiently large even integers can be represented as a pair of eight prime cubes and k powers of $2$. In particular, we prove that $k=335$ is admissible, which improves the previous result.

Keywords

circle methodGoldbach–Linnik problempowers of 2

MSC classification

Primary: 11P32: Goldbach-type theorems; other additive questions involving primes
Secondary: 11P05: Waring's problem and variants 11P55: Applications of the Hardy-Littlewood method
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 2 , October 2023 , pp. 244 - 253
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This work is supported by the National Natural Science Foundation of China (Grant No. 12171286).

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