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Every integer is a sum or difference of 28 integral eighth powers. (English) Zbl 0634.10042

Let v(k) be the least s such that every integer is the sum of s elements of the form \(\pm z^ k\), where z is an integer. Finding bounds for v(k) is sometimes called the “easier” Waring problem. W. H. J. Fuchs and E. M. Wright [Q. J. Math., Oxf. Ser. 10, 190-209 (1939; Zbl 0022.11501)] had shown that 16\(\leq v(8)\leq 30\). It is now proved that 17\(\leq v(8)\leq 28\) and, more generally, that \(2^{n+1}+1\leq v(2^ n)\) for any integer \(n\geq 2\).
Reviewer: B.Garrison

MSC:

11P05 Waring’s problem and variants

Citations:

Zbl 0022.11501
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Full Text: DOI

References:

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