# Asymptotic basis

From Encyclopedia of Mathematics

*asymptotic basis of order $k$*

A sequence of natural numbers and zero, which as a result of its summation repeated $k$ times yields all sufficiently large natural numbers. The number $k$ is called the order of the asymptotic basis. Thus, the sequence of prime numbers is an asymptotic basis of order 4 (I.M. Vinogradov, 1937); the sequence of cubes of natural numbers is an asymptotic basis of order 7 (Yu.V. Linnik, 1942).

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See also Waring problem; Goldbach problem.

**How to Cite This Entry:**

Asymptotic basis.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Asymptotic_basis&oldid=31758

This article was adapted from an original article by B.M. Bredikhin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article