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http://ir.ncue.edu.tw/ir/handle/987654321/17746
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| Title: | Generalized Fermat, Double Fermat and Newton Sequences |
| Authors: | Du, Bau-Sen;Huang, Sen-Shan;Li, Ming-Chia |
| Contributors: | 數學系 |
| Keywords: | Generalized Fermat sequence;Double Fermat sequence;Newton sequence;M�bius inversion formula;Symbolic dynamics;Liouville's formula;Waring's formula;de Polignac's formula |
| Date: | 2003-01
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| Issue Date: | 2013-12-30T06:56:43Z
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| Publisher: | Elsevier |
| Abstract: | 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. |
| Relation: | Journal of Number Theory, 98(1): 172-183 |
| Appears in Collections: | [數學系] 期刊論文
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