Download e-book for kindle: Applications of Fibonacci Numbers: Proceedings of The Second by Heiko Harborth (auth.), A. N. Philippou, A. F. Horadam, G.

By Heiko Harborth (auth.), A. N. Philippou, A. F. Horadam, G. E. Bergum (eds.)

ISBN-10: 9048184479

ISBN-13: 9789048184477

ISBN-10: 940157801X

ISBN-13: 9789401578011

This e-book comprises nineteen papers from one of the twenty-five papers provided on the moment overseas convention on Fibonacci Numbers and Their functions. those papers were chosen after a cautious assessment through renowned referee's within the box, and so they diversity from easy quantity idea to likelihood and statistics. The Fibonacci numbers are their unifying bond. it's expected that this booklet should be priceless to investigate employees and graduate scholars attracted to the Fibonacci numbers and their purposes. October 1987 The Editors Gerald E. Bergum South Dakota nation college Brookings, South Dakota, U.S.A. Andreas N. Philippou college of Patras Patras, Greece Alwyn F. Horadam collage of latest England Armidale, N.S.W., Australia xiii THE ORGANIZING COMMITTEES neighborhood COMMITTEE INTERN A TIONAL COMMITTEE Bergum, G., Chairman Philippou, A. (Greece), Chairman Edgar, H., Co-chalrman Horadam, A. (Australia), Co-chalrman Bergum, G. (U.s.A.) Thoro, D. Kiss, P. (Hungary) Johnson, M. lengthy, C. (U.S.A.) Lange, L.

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Additional resources for Applications of Fibonacci Numbers: Proceedings of The Second International Conference on Fibonacci Numbers and Their Applications’ San Jose State University, California, U.S.A. August 1986

Example text

The existence of a primitive prime factor of terms Rn (n>no) is known (see K. Zsigmondy [111, A. Schinzel [7] and C. L. Stewart [9]). A. Schinzel [6] proved that there are infinitely many indices n for which Rn has at least two primitive prime factors (these n's form an arithmetical progression). But we do not know much more about it. Problem 3 is very hard, we know almost nothing about it. For example, for the Fibonacci sequence F we do not know a prime such that p21F.. would hold if p is Or in another special case, a a primitive prime divisor of Fn.

2 = 0 ( x· 111/2 • ~ I ( ) x· log x). '" og "'Iel el~2 Thus by (4) and (7) we get E"'/2 O(x·log x) = which completes the proof. Proof of Theorem~: We may suppose that x is a positive integer. Let ~ be a real number satisfying 0 < f < 3/(2if2) and let R"I' R"2' . • , R"", be an arrangement of the numbers {R"},,~,,, such that PP(R"I) > PP(RnJ) if i < j. We introduce the notation · . t eger n > 2 h as a t most nc/log log SIDee an ID n d'IS t·IDC t POSI·t·lve d"IVlsors (c is a constant) and naturally /pen) < n, by Lemmas 1, 3 and 4 we get log for any f: IRnl < (1 > 0 and x ~ log Q", > and so + dn· log lal ~ (1 + dx· log lal n > no (d.

Stewart. g. , f3 and k, and cp is the Euler function. Furthermore, for "almost all" integers n, n·log 2 n ) 1 1 ' P(Rn ) > f( n·ogogn n-_ where fen) is any real valued function with 1 i m fCn) = 00. We give a result for the greatest primitive prime power factors of Lucas numbers which will be denoted by PP(Rn). Theorem~: Let x and ). (0 < ). < 1) be real numbers. Let S'" be the set of the terms Rn of a non-degenerate Lucas sequence for which n :;:: x and Rn has a primitive prime power factor greater than n2 ->.

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Applications of Fibonacci Numbers: Proceedings of The Second International Conference on Fibonacci Numbers and Their Applications’ San Jose State University, California, U.S.A. August 1986 by Heiko Harborth (auth.), A. N. Philippou, A. F. Horadam, G. E. Bergum (eds.)


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