Difference between revisions of "Asymptotic basis"
From Encyclopedia of Mathematics
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| − | ''asymptotic basis of order | + | {{TEX|done}} |
| + | ''asymptotic basis of order $k$'' | ||
| − | A sequence of natural numbers and zero, which as a result of its summation repeated | + | 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). |
Latest revision as of 16:33, 15 April 2014
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).
Comments
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
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