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By David V. Chudnovsky, Gregory V. Chudnovsky, Harvey Cohn, Visit Amazon's Melvyn B. Nathanson Page, search results, Learn about Author Central, Melvyn B. Nathanson,

ISBN-10: 3540176691

ISBN-13: 9783540176695

This can be the 3rd Lecture Notes quantity to be produced within the framework of the hot York quantity idea Seminar. The papers contained listed below are mostly examine papers. N

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ATANASSOV K. 1989: Remark on variants of Fibonacci squares. Bulletin of Number Theory and Related Topics Vol. XIII, 25-27. 7. ATANASSOV K. 1989: A remark on a Fibonacci plane. Bulletin of Number Theory and Related Topics Vol. XIII, 69-71. 8. ATANASSOV K. , The Fibonacci Quarterly 33, No. 3, 249-250. 9. , Sasselov D. 1985: A new perspective to the generalization of the Fibonacci sequence. The Fibonacci Quarterly 23, No. 1, 21-28. 10. , Mihov S. 1992: Recurrent formulas of the generalized Fibonacci and Tribonacci sequences.

The following theorem establishes a relationship between these eight sequences and the Fibonacci numbers. 6: For every integer n > 0: (a)ln + tn=Fn-l, The 2-Fibonacci Sequences 15 (6)7^ + ^ = ^ - 1 , (d)ri + 5*=Fn. Proof: (a) If n = 0, then: ^ + ^ = 1 + 0 = ^-1 and jl+6\ = 0 + 0 = FO. Let us assume that the assertion is true for all integers less than or equal to some integer n > 2. 5) and induction hypothesis 7^+1 + <5i+i = = <5i + <£-i + 7n + ln-1 Fn-1 + -Pn-2 = ^tii and, therefore, (a) is true for all integers n > 0.

1(a)). i=0 Hence, (g) is true for all integers k > 0. A similar proof can be given for each of the remaining eleven parts of the theorem. 2. Therefore, the proofs are omitted. fc+2 (c) E (ai-Pi)=0. i=0 As one might suspect, there should be a relationship between the new sequence and the Fibonacci numbers. The next theorem establishes one of these relationships. (ai + Pi). Proof: The statement is obviously true if n = 0 and n = 1. Let us assume that the statement is true for all integers less than or equal to some integer n > 2.

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Number Theory by David V. Chudnovsky, Gregory V. Chudnovsky, Harvey Cohn, Visit Amazon's Melvyn B. Nathanson Page, search results, Learn about Author Central, Melvyn B. Nathanson,


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