| Title:
|
On pairs of Goldbach-Linnik equations with unequal powers of primes (English) |
| Author:
|
Huang, Enxun |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
73 |
| Issue:
|
4 |
| Year:
|
2023 |
| Pages:
|
1219-1228 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is proved that every pair of sufficiently large odd integers can be represented by a pair of equations, each containing two squares of primes, two cubes of primes, two fourth powers of primes and 105 powers of 2. (English) |
| Keyword:
|
Goldbach-Waring-Linnik problem |
| Keyword:
|
circle method |
| Keyword:
|
powers of 2 |
| MSC:
|
11P05 |
| MSC:
|
11P32 |
| MSC:
|
11P55 |
| idZBL:
|
Zbl 07790570 |
| DOI:
|
10.21136/CMJ.2023.0470-22 |
| . |
| Date available:
|
2023-11-23T12:26:36Z |
| Last updated:
|
2026-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151956 |
| . |
| Reference:
|
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| Reference:
|
[2] Kong, Y.: On pairs of linear equations in four prime variables and powers of two.Bull. Aust. Math. Soc. 87 (2013), 55-67. Zbl 1266.11110, MR 3011941, 10.1017/S0004972712000172 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[5] Languasco, A., Zaccagnini, A.: On a Diophantine problem with two primes and $s$ powers of two.Acta Arith. 145 (2010), 193-208. Zbl 1222.11049, MR 2733083, 10.4064/aa145-2-7 |
| Reference:
|
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| Reference:
|
[7] Linnik, Y. V.: Addition of prime numbers with powers of one and the same number.Mat. Sb., N. Ser. 32 (1953), 3-60 Russian. Zbl 0051.03402, MR 0059938 |
| Reference:
|
[8] Liu, J.: Enlarged major arcs in additive problems. II.Proc. Steklov Inst. Math. 276 (2012), 176-192. Zbl 1297.11130, MR 2986119, 10.1134/S0081543812010154 |
| Reference:
|
[9] Liu, Z.: Goldbach-Linnik type problems with unequal powers of primes.J. Number Theory 176 (2017), 439-448. Zbl 1422.11207, MR 3622138, 10.1016/j.jnt.2016.12.009 |
| Reference:
|
[10] Liu, J., Liu, M.-C., Wang, T.: On the almost Goldbach problem of Linnik.J. Théor. Nombres Bordx. 11 (1999), 133-147. Zbl 0979.11051, MR 1730436, 10.5802/jtnb.242 |
| Reference:
|
[11] Lü, X.: On unequal powers of primes and powers of 2.Ramanujan J. 50 (2019), 111-121. Zbl 1472.11269, MR 4008100, 10.1007/s11139-018-0128-2 |
| Reference:
|
[12] Pintz, J., Ruzsa, I. Z.: On Linnik's approximation to Goldbach's problem. I.Acta. Arith. 109 (2003), 169-194. Zbl 1031.11060, MR 1980645, 10.4064/aa109-2-6 |
| Reference:
|
[13] Zhao, L.: On the Waring-Goldbach problem for fourth and sixth powers.Proc. Lond. Math. Soc. (3) 108 (2014), 1593-1622. Zbl 1370.11116, MR 3218320, 10.1112/plms/pdt072 |
| Reference:
|
[14] Zhao, X.: Goldbach-Linnik type problems on cubes of primes.Ramanujan J. 57 (2022), 239-251. Zbl 1498.11203, MR 4360484, 10.1007/s11139-020-00303-9 |
| . |
