Decomposing 40 billion integers by four tetrahedral numbers

Chung Chiang Chou, Yuefan Deng

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)893-901
Number of pages9
JournalMathematics of Computation
Issue number218
StatePublished - Apr 1997


  • Asymptotic form
  • Parallel computing
  • Waring's problem

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


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