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NCUEIR > College of Science > math > Periodical Articles > Item 987654321/15816

Please use this identifier to cite or link to this item: http://ir.ncue.edu.tw/ir/handle/987654321/15816

Title:	Decomposing 40 Billion Integers by Four Tetrahedral Numbers
Authors:	Chou, Chung-Chiang;Deng, Yuefan
Contributors:	數學系
Keywords:	Asymptotic form;Parallel computing;Waring's problem
Date:	1997-04
Issue Date:	2013-03-12T04:07:55Z
Publisher:	American Mathematical Society
Abstract:	Based upon a computer search performed on a massively parallel supercomputer, we found that any integer n less than 40 billion (40B) but greater than 343, 867 can be written as a sum of four or fewer tetrahedral numbers. This result has established a new upper bound for a conjecture compared to an older one, 1B, obtained a year earlier. It also gives more accurate asymptotic forms for partitioning. All this improvement is a direct result of algorithmic advances in efficient memory and cpu utilizations. The heuristic complexity of the new algorithm is O(n) compared with that of the old, O(n5/3 log n).
Relation:	Mathematics of Computation, 66(218): 893-901
Appears in Collections:	[math] Periodical Articles

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