Generalized Fermat, double Fermat and Newton sequences

Baun Sen Du*, Sen Shan Huang, Ming-Chia Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In this paper, we discuss the relationship among the generalized Fermat, double Fermat, and Newton sequences. In particular, we show that every double Fermat sequence is a generalized Fermat sequence, and the set of generalized Fermat sequences, as well as the set of double Fermat sequences, is closed under term-by-term multiplication. We also prove that every Newton sequence is a generalized Fermat sequence and vice versa. Finally, we show that double Fermat sequences are Newton sequences generated by certain sequences of integers. An approach of symbolic dynamical systems is used to obtain congruence identities.

Original languageEnglish
Pages (from-to)172-183
Number of pages12
JournalJournal of Number Theory
Issue number1
StatePublished - 1 Jan 2003


  • de Polignac''s formula
  • Double Fermat sequence
  • Generalized Fermat sequence
  • Liouville's formula
  • Möbius inversion formula
  • Newton sequence
  • Symbolic dynamics
  • Waring's formula

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