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ON THE WARING–GOLDBACH PROBLEM FOR CUBES

Published online by Cambridge University Press:  01 September 2009

JÖRG BRÜDERN
Affiliation:
Institut für Algebra und Zahlentheorie, Universität Stuttgart, D-70511 Stuttgart, Germany e-mail: bruedern@mathematik.uni-stuttgart.de
KOICHI KAWADA
Affiliation:
Department of Mathematics, Faculty of Education, Iwate University, Morioka 020-8550, Japan e-mail: kawada@iwate-u.ac.jp
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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