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Goldbach-Waring problem

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A problem concerning the behaviour of the number of solutions of the equation

where are prime numbers and (cf. Waring problem; Goldbach problem). The results obtained (up to 1977) are roughly the same as those obtained in Waring's problem: It has been proved that the equation is solvable (i.e. ) if , while an asymptotic formula for has been obtained for . These solutions were obtained by the Vinogradov method.

References

[1] I.M. Vinogradov, "The method of trigonometric sums in the theory of numbers" , Interscience (1954) (Translated from Russian)
[2] L.-K. Hua, "Abschätzungen von Exponentialsummen und ihre Anwendung in der Zahlentheorie" , Enzyklopaedie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen , 1 : 2 (1959) (Heft 13, Teil 1)
How to Cite This Entry:
Goldbach-Waring problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Goldbach-Waring_problem&oldid=17140
This article was adapted from an original article by A.A. Karatsuba (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article