## Involve: A Journal of Mathematics

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

### New results on an anti-Waring problem

#### Abstract

The number $N(k,r)$ 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 $N(2,1)=129$, 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 $N(k,r)$. We then use that theorem to find $N(2,r)$ for $1≤r≤50$ and $N(3,r)$ for $1≤r≤30$.

#### 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

#### 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

#### References

• J. Deering and W. Jamieson, “On anti-Waring numbers”, to appear in J. Combin. Math. Combin. Comput.
• P. Johnson and M. Laughlin, “An anti-Waring conjecture and problem”, Int. J. Math. Comput. Sci. 6:1 (2011), 21–26.
• N. Looper and N. Saritzky, “An anti-Waring theorem and proof”, presentation at the MAA undergraduate poster seesion, Boston, January 2012.
• E. Weisstein, “Waring's problem”, http://mathworld.wolfram.com/WaringsProblem.html.