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).
Original language | English (US) |
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Pages (from-to) | 893-901 |
Number of pages | 9 |
Journal | Mathematics of Computation |
Volume | 66 |
Issue number | 218 |
DOIs | |
State | Published - Apr 1997 |
Keywords
- Asymptotic form
- Parallel computing
- Waring's problem
ASJC Scopus subject areas
- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics