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On Waring's problem for intermediate powers

Volume 176 / 2016

Trevor D. Wooley Acta Arithmetica 176 (2016), 241-247 MSC: 11P05, 11P55. DOI: 10.4064/aa8439-8-2016 Published online: 29 September 2016

Abstract

Let $G(k)$ denote the least number $s$ such that every sufficiently large natural number is the sum of at most $s$ positive integral $k$th powers. We show that $G(7)\le 31$, $G(8)\le 39$, $G(9)\le 47$, $G(10)\le 55$, $G(11)\le 63$, $G(12)\le 72$, $G(13)\le 81$, $G(14)\le 90$, $G(15)\le 99$, $G(16)\le 108$.

Authors

  • Trevor D. WooleySchool of Mathematics
    University of Bristol
    University Walk, Clifton
    Bristol BS8 1TW, United Kingdom
    e-mail

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