Waring's problem for pyramidal numbers

Yue Fan Deng, Chen Ning Yang

Research output: Contribution to journalArticlepeer-review


It has been proved that every positive integer is expressible as a sum of no more than eight pyramidal numbers P(m) = (m - 1)m(m + 1) 6. This paper reports on a computer calculation of the partition of integers from n = 1 to 109 into pyramidal numbers. We find that no integer ≤109 needs more than five pyramidal numbers for its partition, and only 241 of them do need five. We define J(n) as the least number of pyramidal numbers to partition n, and Nk(n) as the number of positive integers l less than or equal to n for which J(l) = k. Based on our numerical results we make conjectures about the asymptotic form of Nk(n) for n → ∞.

Original languageEnglish (US)
Pages (from-to)277-283
Number of pages7
JournalScience in China (Scientia Sinica) Series A
Issue number3
StatePublished - Mar 1994


  • Waring's problem
  • asymptotic form
  • parallel computing

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy


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