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Volume 40 Number 1 February 2002

CONTENTS

Cover Page

Referees 2
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Wen-Jin Woan
A Combinatorial Proof of a Recursive Relation of the Motzkin Sequence by Lattice Paths
3
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László Szalay
On the Resolution of the Equations Un = \binom(x, 3) and Vn = \binom(x, 3)
9
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László Tóth
The Probability that k Positive Integers Are Pairwise Relatively Prime
13
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Chu Wenchang
Some Binomial Convolution Formulas
19
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Paul Thomas Young
On Modified Dickson Polynomials
33
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Wayne L. McDaniel
On Fibonacci and Pell Numbers of the Form kx2
41
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Paul J. Andaloro
The 3x+1 Problem and Directed Graphs
43
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Napoleon Gauthier
Book Review: Fibonacci and Lucas Numbers with Applications, by Thomas Koshy
55
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Neville Robbins
An Alternate Proof of a Theorem of J. Ewell
56
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Neville Robbins
On the Number of Partitions into an Even and Odd Number of Parts
57
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Jack Y. Lee
On the Morgan-Voyce Polynomial Generalization of the First Kind
59
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Jan-Christoph Puchta
Representation of Numbers with Negative Digits and Multiplication of Small Integers
66
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Jan-Christoph Puchta
On the Distribution of Totients
68
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R. S. Melham
Reduction Formulas for the Summation of Reciprocals in Certain Second-Order Recurring Sequences
71
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Florian Luca
Consecutive Binomial Coefficients in Pythagorean Triples and Squares in the Fibonacci Sequences
76
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R. B. Taher, M. Mouline, and M. Rachidi
Solving Some General Nonhomogeneous Recurrence Relations of Order r by a Linearization Method and an Application to Polynomial and Factorial Polynomial Cases
79
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Edited by Russ Euler & Jawad Sadek
Elementary Problems and Solutions
85
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Announcement of the Tenth International Conference on Fibonacci Numbers and Their Applications 90
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Edited by Raymond E. Whitney
Advanced Problems and Solutions
91
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Back Cover