### 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(n^{5/3} log n).

Original language | English |
---|---|

Pages (from-to) | 893-901 |

Number of pages | 9 |

Journal | Mathematics of Computation |

Volume | 66 |

Issue number | 218 |

Publication status | Published - 1997 Apr 1 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

### Cite this

*Mathematics of Computation*,

*66*(218), 893-901.

}

*Mathematics of Computation*, vol. 66, no. 218, pp. 893-901.

**Decomposing 40 billion integers by four tetrahedral numbers.** / Chou, Chung-Chiang; Deng, Yuefan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Decomposing 40 billion integers by four tetrahedral numbers

AU - Chou, Chung-Chiang

AU - Deng, Yuefan

PY - 1997/4/1

Y1 - 1997/4/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=0031484553&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031484553&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031484553

VL - 66

SP - 893

EP - 901

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 218

ER -