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

Published online by Cambridge University Press:  14 December 2022

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

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.

Type
Research Article
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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