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

This publication comprises thirty-three papers from one of the thirty-eight papers offered on the Fourth foreign convention on Fibonacci Numbers and Their functions which was once held at Wake woodland collage, Winston-Salem, North Carolina from July 30 to August three, 1990. those papers were chosen after a cautious evaluation by means of renowned referees within the box, and so they variety from hassle-free quantity concept to chance and facts. The Fibonacci numbers and recurrence kinfolk are their unifying bond. it's expected that this e-book, like its 3 predecessors, should be worthwhile to investigate staff and graduate scholars drawn to the Fibonacci numbers and their functions. March 1, 1991 The Editors Gerald E. Bergum South Dakota country collage 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 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 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 record OF participants TO THE convention *ALFORD, CECIL zero. , (coauthor Daniel C. Fielder) "Pascal's Triangle: best Gun or simply one of many Gang?" *ANDERSON, PETER G. , "A Fibonacci-Based Pseudo-Random quantity Generator.

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**Example text**

R2 ra ord a 4. ACKNOWLEDGMENT We wish to thank the referee for his helpful suggestions modifying the statement of Theorem 1, shortening the proof of Theorem 1, and making the paper more concise. REFERENCES [1] Banks, D. " Master's Thesis. University of North Carolina at Chapel Hill, 1987. [2] Carmichael, R. D. " Quart. J. Pure Appl. Math. 48 (1920): pp. 343-372. [3] Robinson, D. W. 2 (1963): pp. 29-37. [4] Robinson, D. W. " Amer. Math. Monthly 73 (1966): pp. 619-621. [5] Somer, L. 4 (1982): pp.

We have for the 512 sums E8 ;=1 . E(k, s, I, c) 2 = 1,640,100, and 8. 2 E E(I, s, r, c) = 1,640,100, ;=1 This same doubly-magic sum holds for the major space diagonals with these new three digit entries. BROKEN DIAGONALS We now explain the uppercase and the lowercase respectively over the columns A and C throughout the 4-Cube. Let I(n, 1, k, s), under some column labeled I, represent the number ADA, on the particular row where it is found, and as well let I(n, 2, k, s) represent DAD, where the indices k and s correspond to cube and square and n = 0, 1, ...

W. " Amer. Math. Monthly 73 (1966): pp. 619-621. [5] Somer, L. 4 (1982): pp. 311-333. [6] Somer, L. D. Thesis. The University of Illinois at Urbana-Champaign, 1985. [7] Wyler, O. " Amer. Math. Monthly 72 (1965): pp. 500-506. NEARLY ISOSCELES TRIANGLES WHERE THE VERTEX ANGLE IS A MULTIPLE OF THE BASE ANGLE Marjorie Bicknell-Johnson 1. cr - ncr TRIANGLES Let a triangle in which the vertex angle is a positive integral multiple n of a base angle be called an cr - ncr triangle. recursive method. We find integral solutions for the lengths of the sides by a We note that, for any particular cr for which there is an integral cr - ncr triangle, cos cr must be a rational number by the law of cosines.