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ON THE WARING–GOLDBACH PROBLEM FOR CUBES

  • JÖRG BRÜDERN (a1) and KOICHI KAWADA (a2)

Abstract

We prove that almost all natural numbers satisfying certain necessary congruence conditions can be written as the sum of two cubes of primes and two cubes of P2-numbers, where, as usual, we call a natural number a P2-number when it is a prime or the product of two primes. From this result we also deduce that every sufficiently large integer can be written as the sum of eight cubes of P2-numbers.

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References

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1.Brüdern, J., A sieve approach to the Waring–Goldbach problem, I: Sums of four cubes, Ann. Scient. École. Norm. Sup. 28 (4) (1995), 461476.
2.Brüdern, J. and Kawada, K., Ternary problems in additive prime number theory, in Analytic number theory (Jia, C. and Matsumoto, K, Editors), Developments in Mathematics, vol. 6 (Kluwer Academic, Dordrecht/Boston/London, 2002), 3991.
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5.Hua, L. K., Additive theory of prime numbers (American Mathematical Society, Providence, RI, 1965).
6.Kawada, K., Note on the sum of cubes of primes and an almost prime, Arch. Math. 69 (1997), 1319.
7.Motohashi, Y., Sieve methods and prime number theory (Tata Institute for Fundamental Research, Bombay, India, 1983).
8.Roth, K. F., On Waring's problem for cubes, Proc. Lond. Math. Soc. 53 (2) (1951), 268279.
9.Vaughan, R. C., The Hardy–Littlewood method, 2nd ed. (Cambridge University Press, Cambridge, 1997).

Keywords

ON THE WARING–GOLDBACH PROBLEM FOR CUBES

  • JÖRG BRÜDERN (a1) and KOICHI KAWADA (a2)

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