Download e-book for iPad: Applications of Fibonacci Numbers: Volume 4 Proceedings of by Peter G. Anderson (auth.), G. E. Bergum, A. N. Philippou, A.

By Peter G. Anderson (auth.), G. E. Bergum, A. N. Philippou, A. F. Horadam (eds.)

ISBN-10: 9401055904

ISBN-13: 9789401055901

ISBN-10: 940113586X

ISBN-13: 9789401135863

This ebook includes thirty-three papers from one of the thirty-eight papers awarded on the Fourth overseas convention on Fibonacci Numbers and Their purposes which used to be held at Wake woodland collage, Winston-Salem, North Carolina from July 30 to August three, 1990. those papers were chosen after a cautious overview by way of renowned referees within the box, and so they diversity from user-friendly quantity thought to likelihood and information. The Fibonacci numbers and recurrence kin are their unifying bond. it truly is expected that this ebook, like its 3 predecessors, might be helpful to investigate employees and graduate scholars attracted to the Fibonacci numbers and their functions. March 1, 1991 The Editors Gerald E. Bergum South Dakota country college Brookings, South Dakota, U. S. A. Alwyn F. Horadam college 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 overseas 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 okay. 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 checklist OF participants 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 info 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

Example text

1), b~, and c~ will develop the common factor b n-2, n > 2, a~, which will have to be removed to keep them relatively prime, making primitive solutions. For now, we can quickly write solutions for small values of n successively by removing common factors by inspection. 2) where an' b n, and cn are sides of an a - na triangle with cn opposite na and an opposite angle a, (an' b n, cn) = 1, which is proved in Section 4. Now, in an a - na triangle, we must have (n + l)a < 180· because we have to leave room for the third angle.

Basic Property: Let m, nand p be positive integers. If there are integers sand t such that p=sm+tn, then (am' an) lap' Proof: Since (m, n) Corollary: I p, a(m,n) I a p' From this and (1), we get the result. Let n t ,"', n. and p be positive integers. If p=ttn t + .. n. for some integers tt' ... , then we have (an' ... , an ) I a p ' and therefore, we have t • Remark 1: As the SDS is a DS, every term of the SDS is divisible by its initial term at. Hence, we can assume a 1=1 as long as we stay with the GCD or LCM equalities concerning the generalized binomial or multinomial coefficients and their modifications.

ARKIN, D. C. ARNEY, F. R. GIORDANO AND R. A. ), (v=mP+t), holds for m = 0, 1,2, ... ) (w=p ra) for any integer a. ). In this paper, we put (f(X))k = C(k,O) + C(k,l)x + C(k,2)x 2 + ... + C(k,n)x" + ... 1) f(x) = E~=o (2av+b)x tl ( av +b). 2) such that Theorem: Let P = 4am+3 be a prime. 3) 2 for n == - 2m - d (mod P) where d is an integer and d = b +3)/2a. Further, since b is odd, b = 2w+l makes 2(w 2 + w + 1) = ad. 2), we get Now, let n=uP - 2m - dj then C(2,n) is the coefficient of x uP in the expansion of x d + 2m (f(x))2.

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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.)


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