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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
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Abstract |
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The number is defined to be the first integer such that it and every subsequent integer can be written as the sum of the -th powers of or more distinct positive integers. For example, it is known that , 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 . We then use that theorem to find for and for . |
Keywords
number theory, Waring, anti-Waring, series
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Mathematical Subject Classification 2010
Primary: 11A67
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Milestones
Received: 24 April 2013
Revised: 10 July 2013
Accepted: 24 July 2013
Published: 16 November 2013
Communicated by Nigel Boston
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Authors |
| Chris Fuller | |
| Department of Mathematics Cumberland University Lebanon, TN 37087 United States |
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| David R. Prier | |
| Department of Mathematics Gannon University Erie, PA 16541-0001 United States |
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| Karissa A. Vasconi | |
| 1440 Heinz Avenue Sharon, PA 16146 United States |
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