Volume 4, 1998, Number 4

Volume 4Number 1Number 2Number 3 ▷ Number 4


Preface: John Christopher Turner
Editorial. Pages 129—134
Editorial (PDF, 6202 Kb)

The Fibonacci track form, with applications in Fibonacci vector geometry
Original research paper. Pages 135—147
J. C. Turner
Full paper (PDF, 8187 Kb) | Abstract

A particular form of generalized Fibonacci sequence is defined, and supplied with the generic name track. Reasons for doing this are discussed, and simple examples of tracks are given. Then an example which occurs in Fibonacci Vector Geometry, namely the vector-product track, is treated in some detail.

Some representations related to n!
Original research paper. Pages 148—153
Mladen V. Vassilev-Missana and Krassimir T. Atanassov
Full paper (PDF, 3541 Kb)

Circumferences with golden points
Original research paper. Pages 154—156
Vassia K. Atanassova
Full paper (PDF, 1536 Kb)

Some observations on the Diophantine equation u2 + v2 = x3 + y3
Original research paper. Pages 157—159
J. H. Clarke and A. G. Shannon
Full paper (PDF, 1926 Kb)

Diophantine quadruples and quintuples modulo 4
Original research paper. Pages 160—164
Andrej Dujella
Full paper (PDF, 2596 Kb) | Abstract

A Diophantine m-tuple with the property D(n) is a set { a1, a2 , … am} of positive integers such that for 1 ≤ i < jm, the number aiaj + n is a perfect square. In the present paper we give necessary conditions that the elements a1 of a set {a1, a2, a3, a4, a5, a6} must satisfy modulo 4 in order to be a Diophantine quintuple.

Fibonacci numbers with modular rings
Original research paper. Pages 165—174
J. V. Leyendekkers and A. G. Shannon
Full paper (PDF, 6568 Kb)

On the 61-st, the 62-nd, and the 63-rd Smarandache’s problems
Original research paper. Pages 175—182
Krassimir T. Atanassov
Full paper (PDF, 4281 Kb)


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