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

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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 1r50 and N(3,r) for 1r30.

Article information

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

Received: 24 April 2013
Revised: 10 July 2013
Accepted: 24 July 2013
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11A67: Other representations

number theory Waring anti-Waring series


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.

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