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題 名 | Investigating Fibonacci Sequence Properties for Theoretical Computer Science |
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作 者 | Wu, Chia-long; Wu, Ching-seh; | 書刊名 | 危機管理學刊 |
卷 期 | 2:1 民94.03 |
頁 次 | 頁19-26 |
分類號 | 312.76 |
關鍵詞 | Algorithmic number theory; Elementary cryptography; Information science; Primality proving; Recurrence relation; |
語 文 | 英文(English) |
英文摘要 | The Fibonacci sequence has played dominant roles in many branches of science and engineering. This sequence not only has an amazing number of applications in nature, but also has a tremendous number of interesting properties. The main object of this paper is to propose a systematic investigation of the familiar Fibonacci sequence in number theory and present a heuristic derivation of their properties. In this paper, we not only analyze the basic concepts and definitions of recurrence functions, generating functions, continued fractions, the Golden ratio, and primality test, but also give detailed analysis and further discussions for them with a different point of view when they incorporated with the Fibonacci sequence. Based on these concepts and definitions, we engage to contribute exact theorem descriptions and proofs. Moreover, extended properties including recurrence relations, summation formulas, and primality proving issues related to Fibonacci sequence are systematically studied and further explored. |
本系統中英文摘要資訊取自各篇刊載內容。