Vol. 7, No. 2, 2014

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New results on an anti-Waring problem

Chris Fuller, David R. Prier and Karissa A. Vasconi

Vol. 7 (2014), No. 2, 239–244

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.

number theory, Waring, anti-Waring, series
Mathematical Subject Classification 2010
Primary: 11A67
Received: 24 April 2013
Revised: 10 July 2013
Accepted: 24 July 2013
Published: 16 November 2013

Communicated by Nigel Boston
Chris Fuller
Department of Mathematics
Cumberland University
Lebanon, TN 37087
United States
David R. Prier
Department of Mathematics
Gannon University
Erie, PA 16541-0001
United States
Karissa A. Vasconi
1440 Heinz Avenue
Sharon, PA 16146
United States