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.
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@article{CRMATH_2020__358_4_393_0, author = {Liu, Yuhui}, 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}, url = {http://www.numdam.org/articles/10.5802/crmath.5/} }
TY - JOUR AU - Liu, Yuhui TI - On pairs of equations involving unlike powers of primes and powers of 2 JO - Comptes Rendus. Mathématique PY - 2020 SP - 393 EP - 400 VL - 358 IS - 4 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.5/ DO - 10.5802/crmath.5 LA - en ID - CRMATH_2020__358_4_393_0 ER -
%0 Journal Article %A Liu, Yuhui %T On pairs of equations involving unlike powers of primes and powers of 2 %J Comptes Rendus. Mathématique %D 2020 %P 393-400 %V 358 %N 4 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.5/ %R 10.5802/crmath.5 %G en %F CRMATH_2020__358_4_393_0
Liu, Yuhui. On pairs of equations involving unlike powers of primes and powers of 2. Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 393-400. doi : 10.5802/crmath.5. http://www.numdam.org/articles/10.5802/crmath.5/
[1] On pairs of equations in unlike powers of primes and powers of 2, Open Math., Volume 15 (2017), pp. 1487-1494 | MR | Zbl
[2] Prime numbers and powers of two, Tr. Mat. Inst. Steklova, Volume 38 (1951), pp. 151-169 (in Russian) | MR
[3] 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] 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] Squares of primes and powers of 2, Monatsh. Math., Volume 128 (1999) no. 4, pp. 283-313 | MR | Zbl
[6] Goldbach–Linnik type problems with unequal powers of primes, J. Number Theory, Volume 176 (2017), pp. 439-448 | MR | Zbl
[7] On unlike powers of primes and powers of 2, Acta Math. Hung., Volume 132 (2011) no. 1-2, pp. 125-139 | MR | Zbl
[8] On sum of one prime, two squares of primes and powers of 2, Monatsh. Math., Volume 187 (2017) no. 1, pp. 113-123 | DOI | MR | Zbl
[9] On unequal powers of primes and powers of 2, Ramanujan J., Volume 50 (2019) no. 1, pp. 111-121 | MR | Zbl
[10] Linnik’s approximation to Goldbach’s conjecture, and other problems, J. Number Theory, Volume 153 (2015), pp. 54-62 | DOI | MR | Zbl
[11] Some results on Waring-Goldbach type problems, Ph. D. Thesis, University of Hong Kong (2012) | DOI
[12] 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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