## Involve: A Journal of Mathematics

- Involve
- Volume 7, Number 2 (2014), 239-244.

### New results on an anti-Waring problem

Chris Fuller, David Prier, and Karissa Vasconi

#### Abstract

The number $N\left(k,r\right)$ is defined to be the first integer such that it and every subsequent integer can be written as the sum of the $k$-th powers of $r$ or more distinct positive integers. For example, it is known that $N\left(2,1\right)=129$, and thus the last number that cannot be written as the sum of one or more distinct squares is 128. We give a proof of a theorem that states if certain conditions are met, a number can be verified to be $N\left(k,r\right)$. We then use that theorem to find $N\left(2,r\right)$ for $1\le r\le 50$ and $N\left(3,r\right)$ for $1\le r\le 30$.

#### Article information

**Source**

Involve, Volume 7, Number 2 (2014), 239-244.

**Dates**

Received: 24 April 2013

Revised: 10 July 2013

Accepted: 24 July 2013

First available in Project Euclid: 20 December 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.involve/1513733660

**Digital Object Identifier**

doi:10.2140/involve.2014.7.239

**Mathematical Reviews number (MathSciNet)**

MR3133722

**Zentralblatt MATH identifier**

1291.11021

**Subjects**

Primary: 11A67: Other representations

**Keywords**

number theory Waring anti-Waring series

#### Citation

Fuller, Chris; Prier, David; Vasconi, Karissa. New results on an anti-Waring problem. Involve 7 (2014), no. 2, 239--244. doi:10.2140/involve.2014.7.239. https://projecteuclid.org/euclid.involve/1513733660