On Waring's problem for intermediate powers
Volume 176 / 2016
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 $G(7)\le 31$, $G(8)\le 39$, $G(9)\le 47$, $G(10)\le 55$, $G(11)\le 63$, $G(12)\le 72$, $G(13)\le 81$, $G(14)\le 90$, $G(15)\le 99$, $G(16)\le 108$.
