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Goldbach-Linnik type problems with unequal powers of primes

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초록

It is proved that every sufficiently large even integer can be represented as a sum of two squares of primes, two cubes of primes, two fourth powers of primes and 17 powers of 2.

Abstract

It is proved that every sufficiently large even integer can be represented as a sum of two squares of primes, two cubes of primes, two fourth powers of primes and 17 powers of 2.

참고문헌 (19)

  1. P. X. Gallagher, "Primes and powers of 2", Invent. Math, 29(2), pp.125~142 (1975)[DOI]
  2. G. H. Hardy, "An Introduction to the Theory of Numbers" (2008), Oxford University Press
  3. D. R. Heath-Brown, "Integers represented as a sum of primes and powers of two", Asian J. Math, 6(3), pp.535~565 (2002)[DOI]
  4. K. Ireland, "A Classical Introduction to Modern Number Theory" (1990), Springer-Verlag
  5. H. Li, "The number of powers of 2 in a representation of large even integers by sums of such powers and of two primes", Acta Arith, 92(3), pp.229~237 (2000)[DOI]
  6. H. Li, "The number of powers of 2 in a representation of large even integers by sums of such powers and of two primes. II", Acta Arith, 96(4), pp.369~379 (2001)[DOI]
  7. Yu. V. Linnik, "Prime numbers and powers of two", Trudy Nat. Inst. Steklov, 38, pp.152~169 (1951), Izdat. Akad. Nauk SSSR
  8. Yu. V. Linnik, "Addition of prime numbers with powers of one and the same number", Mat. Sbornik N.S, 32(74), pp.3~60 (1953)
  9. Z. Liu, "Goldbach-Linnik type problems with unequal powers of primes", J. Number Theory, 176, pp.439~448 (2017)[DOI]
  10. J. Liu, "The number of powers of 2 in a representation of large even integers. II", Sci. China Ser. A, 41(12), pp.1255~1271 (1998)[DOI]
  11. Z. Liu, "Density of two squares of primes and powers of 2", Int. J. Number Theory, 7(5), pp.1317~1329 (2011)[DOI]
  12. X. Lü, "On unequal powers of primes and powers of 2", Ramanujan J, 50(1), pp.111~121 (2019)[DOI]
  13. J. Pintz, "On Linnik’s approximation to Goldbach’s problem. I", Acta Arith, 109(2), pp.169~194 (2003)[DOI]
  14. J. Pintz, "On Linnik’s approximation to Goldbach’s problem. II", Acta Math. Hungar, 161(2), pp.569~582 (2020)[DOI]
  15. D. J. Platt, "Linnik’s approximation to Goldbach’s conjecture, and other problems", J. Number Theory, 153, pp.54~62 (2015)[DOI]
  16. R. C. Vaughan, "The Hardy-Littlewood Method" (1997), Cambridge University Press
  17. T. Wang, "On Linnik’s almost Goldbach theorem", Sci. China Ser. A, 42(11), pp.1155~1172 (1999)[DOI]
  18. L. Zhao, "On the Waring-Goldbach problem for fourth and sixth powers", Proc. Lond. Math. Soc, 108(6), pp.1593~1622 (2014)[DOI]
  19. Xiaodong Zhao, "Goldbach–Linnik type problems on cubes of primes", The Ramanujan Journal, 57(1), pp.239~251 (2020), Springer Science and Business Media LLC[DOI]

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