Comptes Rendus
no. 4
Number Theory
On pairs of equations involving unlike powers of primes and powers of 2
Yuhui Liu1
1School of Mathematical Sciences, Tongji University, Shanghai, 200092, P. R. China
Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 393-400

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:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.5
Classification: 11P32, 11P55

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
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
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     language = {en},
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[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

[2] Yuriĭ V. Linnik Prime numbers and powers of two, Tr. Mat. Inst. Steklova, Volume 38 (1951), pp. 151-169 (in Russian) | MR

[3] Yuriĭ V. Linnik Addition of prime numbers with powers of one and the same number, Mat. Sb., N. Ser., Volume 32 (1953), pp. 3-60 (in Russian) | MR

[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

[5] Jian Ya Liu; Ming-Chit Liu; Tao Zhan Squares of primes and powers of 2, Monatsh. Math., Volume 128 (1999) no. 4, pp. 283-313 | MR | Zbl

[6] Zhi Xin Liu Goldbach–Linnik type problems with unequal powers of primes, J. Number Theory, Volume 176 (2017), pp. 439-448 | MR | Zbl

[7] Zhi Xin Liu; Guang Shi Lü On unlike powers of primes and powers of 2, Acta Math. Hung., Volume 132 (2011) no. 1-2, pp. 125-139 | MR | Zbl

[8] Guang Shi Lü On sum of one prime, two squares of primes and powers of 2, Monatsh. Math., Volume 187 (2017) no. 1, pp. 113-123 | MR | Zbl | DOI

[9] Xiao Dong Lü On unequal powers of primes and powers of 2, Ramanujan J., Volume 50 (2019) no. 1, pp. 111-121 | MR | Zbl

[10] David J. Platt; Timothy S. Trudgian Linnik’s approximation to Goldbach’s conjecture, and other problems, J. Number Theory, Volume 153 (2015), pp. 54-62 | MR | DOI | Zbl

[11] Li Lu Zhao Some results on Waring-Goldbach type problems, Ph. D. Thesis, University of Hong Kong (2012) | DOI

[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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