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The Additive Completion of kth Powers

โœ Scribed by Wenguang Zhai

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
97 KB
Volume
79
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

Let k 2 be a fixed integer. For positive integers M N, let S k (M, N) denote the set of all sets A/[0, M] such that, for all positive integers n N, n can be written as n=a+b k with a # A and b a positive integer. Define

Given =>0, we prove that there exists a $>0 such that for all sufficiently large N f k ($N, N) (k&=) N 1&1ร‚k .

๐Ÿ“œ SIMILAR VOLUMES

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โœ T.D. Browning ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 237 KB

Let k55 be an integer, and let x51 be an arbitrary real number. We derive a bound for the number of positive integers less than or equal to x which can be represented as a sum of two non-negative coprime kth powers, in essentially more than one way.

The kth Laplacian eigenvalue of a tree
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## Abstract Let ฮป~__k__~(__G__) be the __k__th Laplacian eigenvalue of a graph __G__. It is shown that a tree __T__ with __n__ vertices has $\lambda\_{k}(T)\le \lceil { {n}\over{k}}\rceil$ and that equality holds if and only if __k__ < __n__, __k__|__n__ and __T__ is spanned by __k__ vertex disjoin