On pairs of equations involving unlike powers of primes and powers of 2

Yuhui Liu

doi:10.5802/crmath.5

Number Theory

On pairs of equations involving unlike powers of primes and powers of 2

Yuhui Liu ¹

¹ School of Mathematical Sciences, Tongji University, Shanghai, 200092, P. R. China

Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 393-400.

Abstract

In this paper, it is proved that every pair of sufficiently large even integers can be represented by a pair of equations, each containing one prime, one prime square, two prime cubes and 302 powers of 2. This result constitutes a refinement upon that of L. Q. Hu and L. Yang.

Received: 2019-12-19
Revised: 2020-02-09
Accepted: 2020-02-10
Published online: 2020-07-28

DOI: 10.5802/crmath.5

Classification: 11P32, 11P55

Author's affiliations:

Yuhui Liu ¹

¹ School of Mathematical Sciences, Tongji University, Shanghai, 200092, P. R. China

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Yuhui Liu},
     title = {On pairs of equations involving unlike powers of primes and powers of 2},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {393--400},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {4},
     year = {2020},
     doi = {10.5802/crmath.5},
     language = {en},
}

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Yuhui Liu. On pairs of equations involving unlike powers of primes and powers of 2. Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 393-400. doi : 10.5802/crmath.5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.5/

References
Cited by

[1] Li Qun Hu; Li Yang On pairs of equations in unlike powers of primes and powers of 2, Open Math., Volume 15 (2017), pp. 1487-1494 | MR | Zbl

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[4] Jian Y. Liu; Ming-Chit Liu Representation of even integers by cubes of primes and powers of 2, Acta Math. Hung., Volume 91 (2001) no. 3, pp. 217-243 | MR | Zbl

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[12] Li Lu Zhao On unequal powers of primes and powers of 2, Acta Math. Hung., Volume 146 (2015) no. 2, pp. 405-420 | DOI | MR | Zbl

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