By Peter G. Anderson (auth.), G. E. Bergum, A. N. Philippou, A. F. Horadam (eds.)
This e-book comprises thirty-three papers from one of the thirty-eight papers provided on the Fourth foreign convention on Fibonacci Numbers and Their purposes which was once held at Wake wooded area college, Winston-Salem, North Carolina from July 30 to August three, 1990. those papers were chosen after a cautious assessment via popular referees within the box, and so they variety from easy quantity concept to chance and facts. The Fibonacci numbers and recurrence relatives are their unifying bond. it really is expected that this publication, like its 3 predecessors, may be worthwhile to investigate staff and graduate scholars attracted to the Fibonacci numbers and their purposes. March 1, 1991 The Editors Gerald E. Bergum South Dakota kingdom collage Brookings, South Dakota, U. S. A. Alwyn F. Horadam collage of recent England Armidale, N. S. W. , Australia Andreas N. Philippou Minister of schooling Ministry of schooling Nicosia, Cyprus xv THE ORGANIZING COMMITTEES neighborhood COMMITTEE foreign COMMITTEE Howard, Fred T. , Co-Chair Horadam, A. F. (Australia), Co-Chair Waddill, Marcellus E. , Co-Chair Philippou, A. N. (Cyprus), Co-Chair Hayashi, Elmer ok. Ando, S. (Japan) Bergum, G. E. (U. S. A. ) Vaughan, Theresa Harrell, Deborah Bicknell-Johnson, M. B. (U. S. A. ) Campbell, Colin (Scotland) Filipponi, Piero (Italy) Kiss, P. (Hungary) Turner, J. C. (New Zealand) xvii record OF individuals TO THE convention *ALFORD, CECIL zero. , (coauthor Daniel C. Fielder) "Pascal's Triangle: most sensible Gun or simply one of many Gang?" *ANDERSON, PETER G. , "A Fibonacci-Based Pseudo-Random quantity Generator.
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Extra resources for Applications of Fibonacci Numbers: Volume 4 Proceedings of ‘The Fourth International Conference on Fibonacci Numbers and Their Applications’, Wake Forest University, N.C., U.S.A., July 30–August 3, 1990
4). Of the many special cases possible using the Theorem above, we state some results of Arkin, Jacobi, and Ramanujan. 1). 1 ) and among other things that p(-1)(7m+5) _ 0 (mod 7). 2) is a well-known congruence of Ramanujan , but proved in a different way. ACKNOWLEDGEMENTS The authors wish to thank the referee for his very valuable help in setting up this paper and we thank the editor for his patience and interest. 36 J. ARKIN, D. C. ARNEY, F. R. GIORDANO AND R. A. KOLB REFERENCES  Arkin, J.
Bergum, Kluwer Academic Publishers, (1990) pp. 15-26. [4) Hillman, A. P. and Hoggatt, V. E. Jr. " The Fibonacci Quarterly, 10 (1972): pp. 565-568, 598. [5) Hitotumatu, S. and Sato, D. " The Fibonacci Quarterly [6) Hoggatt, V. E. Jr. and Alexanderson, G. L. " 13 (1975): p. 70. The Fibonacci Quarterly, 9 (1971): pp. 351-356, 420-421. [7) Kimberling, C. " The Fibonacci Quarterly 16 (1978): pp. 541-544. [8) Sato, D. " Personal Communication. [9) Ward, M. " Bull. Amer. Math. Soc. 42 (1936) pp. 843845.
19 (1919): pp. 207-210. PERIOD PATTERNS OF CERTAIN SECOND-ORDER LINEAR RECURRENCES MODULO A PRIME David Banks and Lawrence Somer 1. INTRODUCTION Throughout this paper, p will denote a fixed prime. Let a and h be integers and let the Lucas sequence u(a,h) denote the second-order linear recurrence satisfying (1) with initial terms Uo = 0, u1 = 1. Let JJ( a, h) denote the period of u(a, h) modulo p. It is known (see [2, pages 344-345]) that if h"l= 0 (mod p), then u(a,h) is purely periodic modulo p.
Applications of Fibonacci Numbers: Volume 4 Proceedings of ‘The Fourth International Conference on Fibonacci Numbers and Their Applications’, Wake Forest University, N.C., U.S.A., July 30–August 3, 1990 by Peter G. Anderson (auth.), G. E. Bergum, A. N. Philippou, A. F. Horadam (eds.)