Download Applications of Fibonacci Numbers: Proceedings of The Second by Heiko Harborth (auth.), A. N. Philippou, A. F. Horadam, G. PDF

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

This e-book includes nineteen papers from one of the twenty-five papers awarded on the moment overseas convention on Fibonacci Numbers and Their purposes. those papers were chosen after a cautious evaluation by way of renowned referee's within the box, and so they variety from ordinary quantity idea to chance and statistics. The Fibonacci numbers are their unifying bond. it truly is expected that this publication might be invaluable to analyze staff and graduate scholars drawn to the Fibonacci numbers and their functions. October 1987 The Editors Gerald E. Bergum South Dakota kingdom college Brookings, South Dakota, U.S.A. Andreas N. Philippou college of Patras Patras, Greece Alwyn F. Horadam college 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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Extra 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

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To appear. [5] Kishore, N. " Proc. Amer. Math. Soc. 14 (1963): pp 521-533. [6] Kishore, N. " Proc. Amer. Math. Soc. 15 (1964): pp 911-911. [7] Kummer, E. " J. Reine Angeu. Math. 44 (1852): pp 93-146. [8] Lucas, E. "Sur les congruences des nombres euleriens et des coefficients differentiels ..... Bull. Soc. Hath. France 6 (1878): pp 49-54. Kenji Nagasaka and Shiro Ando SYMMETRIC RECURSIVE SEQUENCES MOD M Distribution properties of integer sequences have been widely studied from various points of view.

2): The group T(m) has order the modulus of: 50 C. CAMPBELL, ET AL. 3 , m - 2n, n even. 3 , m - 2n, n odd. , m odd, (m, 3) - 1. , m odd, (m. 3) - 3. 3 if n is even. 3 if n is odd. We shall return to the groups T(m) in the next section. shown to be infinite if (n. 3) - 3 (10). Q, 12) that yen) is isomorphic to the group X(n) with presentation: if (n. 3) - 1. X(n) is a factor Iroup of X(n) by a central subgroup of order 2. Q, 12) show that the conjecture is true for -10 ~ n :;;:: 10 with (n, 3) = 1.

J is a zero of the polynomial (2), we may write (5) We now apply the multinomial theorem to the expression on the right of (5). The number of terms in this expansion depends on the number of non-zero coefficients ar • For notational simplicity, we will assume that each ar ~ O. This does not affect the generality of our results. •• , n.. such that no + ••. + n.. = p. We first prove the following result. • , n.. are non-negative integers such that no + . . + n. • 41 pI --::----'----:, == 0 (mod p), (7) nol • .

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