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Keywords:
Goldbach-Waring-Linnik problem; circle method; powers of 2
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.
References:
[1] Heath-Brown, D. R., Puchta, J.-C.: Integers represented as a sum of primes and powers of two. Asian J. Math. 6 (2002), 535-565. DOI 10.4310/AJM.2002.v6.n3.a7 | MR 1946346 | Zbl 1097.11050
[2] Kong, Y.: On pairs of linear equations in four prime variables and powers of two. Bull. Aust. Math. Soc. 87 (2013), 55-67. DOI 10.1017/S0004972712000172 | MR 3011941 | Zbl 1266.11110
[3] Kong, Y., Liu, Z.: On pairs of Goldbach-Linnik equations. Bull. Aust. Math. Soc. 95 (2017), 199-208. DOI 10.1017/S000497271600071X | MR 3614942 | Zbl 1381.11098
[4] Kumchev, A. V.: On Weyl sums over primes and almost primes. Mich. Math. J. 54 (2006), 243-268. DOI 10.1307/mmj/1156345592 | MR 2252758 | Zbl 1137.11054
[5] Languasco, A., Zaccagnini, A.: On a Diophantine problem with two primes and $s$ powers of two. Acta Arith. 145 (2010), 193-208. DOI 10.4064/aa145-2-7 | MR 2733083 | Zbl 1222.11049
[6] Linnik, Y. V.: Prime numbers and powers of two. Tr. Mat. Inst. Steklova 38 (1951), 152-169 Russian. MR 0050618 | Zbl 0049.31402
[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. MR 0059938 | Zbl 0051.03402
[8] Liu, J.: Enlarged major arcs in additive problems. II. Proc. Steklov Inst. Math. 276 (2012), 176-192. DOI 10.1134/S0081543812010154 | MR 2986119 | Zbl 1297.11130
[9] Liu, Z.: Goldbach-Linnik type problems with unequal powers of primes. J. Number Theory 176 (2017), 439-448. DOI 10.1016/j.jnt.2016.12.009 | MR 3622138 | Zbl 1422.11207
[10] Liu, J., Liu, M.-C., Wang, T.: On the almost Goldbach problem of Linnik. J. Théor. Nombres Bordx. 11 (1999), 133-147. DOI 10.5802/jtnb.242 | MR 1730436 | Zbl 0979.11051
[11] Lü, X.: On unequal powers of primes and powers of 2. Ramanujan J. 50 (2019), 111-121. DOI 10.1007/s11139-018-0128-2 | MR 4008100 | Zbl 1472.11269
[12] Pintz, J., Ruzsa, I. Z.: On Linnik's approximation to Goldbach's problem. I. Acta. Arith. 109 (2003), 169-194. DOI 10.4064/aa109-2-6 | MR 1980645 | Zbl 1031.11060
[13] Zhao, L.: On the Waring-Goldbach problem for fourth and sixth powers. Proc. Lond. Math. Soc. (3) 108 (2014), 1593-1622. DOI 10.1112/plms/pdt072 | MR 3218320 | Zbl 1370.11116
[14] Zhao, X.: Goldbach-Linnik type problems on cubes of primes. Ramanujan J. 57 (2022), 239-251. DOI 10.1007/s11139-020-00303-9 | MR 4360484 | Zbl 1498.11203
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