**Volume 18** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**In Memoriam: Prof. Antal Bege (1962–2012)**

*Editorial. Pages 1—4*

J. Sándor

Editorial (PDF, 107 Kb)

**A modification of an elementary numerical inequality**

*Original research paper. Pages 5—7*

Krassimir Atanassov

Full paper (PDF, 109 Kb) | Abstract

*a*

_{0},

*a*

_{1}, …,

*a*(

_{n}*n*≥ 1):

This is a modification of an inequality, previously introduced by the author.

**Odd-powered triples and Pellian sequences**

*Original research paper. Pages 8—12*

J. V. Leyendekkers and A. G. Shannon

Full paper (PDF, 123 Kb) | Abstract

*N*in the modular ring

^{m}*Z*

_{4}have rows with elements which satisfy Pellian recurrence relations from which Pythagorean triples can form when

*m*= 2. When

*m*is odd, they have different and incompatible Pellian row structure and triples are not formed.

**Fibonacci numbers at most one away from a product of factorials**

*Original research paper. Pages 13—19*

Diego Marques

Full paper (PDF, 166 Kb) | Abstract

*F*)

_{n}_{n≥0}be the Fibonacci sequence given by

*F*

_{0}= 0;

*F*

_{1}= 1 and

*F*

_{n+2}=

*F*

_{n+1}+

*F*, for

_{n}*n*≥ 0. In this note, we find all solutions of the Diophantine equation

*m*

_{1}! …

*m*! ± 1 =

_{k}*F*, where 2 ≤

_{m}*m*

_{1}≤ … ≤

*m*and

_{k}*m*≥ 3.

**Isomorphism testings for graph C_{G}(a, b)**

*Original research paper. Pages 20—34*

Worrawate Leela-Apiradee and Yotsanan Meemark

Full paper (PDF, 234 Kb) | Abstract

*G*be a finite abelian group such that

*G*≠ {0} and

*a*,

*b*∈

*G*\ {0}. Let

*C*(

_{G}*a*,

*b*) be the graph whose vertex set is G and the edge set is given by

*E*= {{

*x*,

*x + a*}, {

*x,*

*x + b*}, {

*x*,

*x − a*}, {

*x*,

*x − b*} :

*x*∈

*G*}.

In this work, we use the properties of finite abelian group to derive isomorphism testing on the graph

*C*(

_{G}*a*,

*b*) defined above. We study classes of isomorphic graphs. This work generalizes Nicoloso and Pietropaoli’s paper .

**A new elementary proof of the inequality φ(n) > π (n)**

*Original research paper. Pages 35—37*

Carlo Sanna

Full paper (PDF, 131 Kb) | Abstract

*φ*(

*n*) >

*π*(

*n*) holds for all integers

*n*≥ 91, an old result of

*L*. Moser. Our proof is based on Bonse’s Inequality. This makes it somewhat simpler than Moser’s proof, which in turn relies on Bertrand’s Postulate.

**Generalized differential operators**

*Original research paper. Pages 38—44*

A. G. Shannon

Full paper (PDF, 44 Kb) | Abstract

**A note on sumsets and difference sets in ℤ/nℤ**

*Original research paper. Pages 45—47*

Christopher J. Richardson and Craig V. Spencer

Full paper (PDF, 168 Kb) | Abstract

*The Irrationals: A Story of the Numbers You Can’t Count On *by Julian Havil

*Book review. Page 48*

Anthony Shannon

Book review (PDF, 107 Kb)