TY - JOUR

T1 - Generalized Fermat, double Fermat and Newton sequences

AU - Du, Baun Sen

AU - Huang, Sen Shan

AU - Li, Ming-Chia

PY - 2003/1/1

Y1 - 2003/1/1

N2 - 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.

AB - 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.

KW - de Polignac''s formula

KW - Double Fermat sequence

KW - Generalized Fermat sequence

KW - Liouville's formula

KW - Möbius inversion formula

KW - Newton sequence

KW - Symbolic dynamics

KW - Waring's formula

UR - http://www.scopus.com/inward/record.url?scp=0037265327&partnerID=8YFLogxK

U2 - 10.1016/S0022-314X(02)00025-2

DO - 10.1016/S0022-314X(02)00025-2

M3 - Article

AN - SCOPUS:0037265327

VL - 98

SP - 172

EP - 183

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -