Almost equal summands in Waring’s problem with shifts

Kirsti D. Biggs

doi:10.1007/s00605-018-1178-7

Almost equal summands in Waring’s problem with shifts

Kirsti D. Biggs^*

^*Corresponding author for this work

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Abstract

A result of Wright from 1937 shows that there are arbitrarily large natural numbers which cannot be represented as sums of skth powers of natural numbers which are constrained to lie within a narrow region. We show that the analogue of this result holds in the shifted version of Waring’s problem.

Original language	English
Number of pages	5
Journal	Monatshefte für Mathematik
Early online date	21 Mar 2018
DOIs	https://doi.org/10.1007/s00605-018-1178-7
Publication status	E-pub ahead of print - 21 Mar 2018

Keywords

Diophantine inequalities
Shifted integers
Waring’s problem

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abstract = "A result of Wright from 1937 shows that there are arbitrarily large natural numbers which cannot be represented as sums of skth powers of natural numbers which are constrained to lie within a narrow region. We show that the analogue of this result holds in the shifted version of Waring{\textquoteright}s problem.",

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Almost equal summands in Waring’s problem with shifts

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