**Volume 20** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4 ▷ Number 5

**Preface**

*Editorial*

Editorial (PDF, 64 Kb)

**A note on the Diophantine equations x_{1}^{k} + x_{2}^{k} + x_{3}^{k} + x_{4}^{k} = 2y_{1}^{k} + 2y_{2}^{k} , k = 3, 6**

*Original research paper. Pages 1–10*

Farzali Izadi, Foad Khoshnam and Arman Shamsi Zargar

Full paper (PDF, 178 Kb) | Abstract

**A note on certain inequalities for bivariate means**

*Original research paper. Pages 11–13*

József Sándor

Full paper (PDF, 123 Kb) | Abstract

**The four roots lemma**

*Original research paper. Pages 14–19*

Kristijan Tabak

Full paper (PDF, 172 Kb) | Abstract

*, we manage to prove that a norm of a sum of any four mutually different roots has to be different that 2.*

^{n}**On integer solutions of A^{5} + B^{3} = C^{5} + D^{3}**

*Original research paper. Pages 20–24*

Farzali Izadi and Arman Shamsi Zargar

Full paper (PDF, 154 Kb) | Abstract

**On upper Hermite–Hadamard inequalities for geometric-convex and log-convex functions**

*Original research paper. Pages 25–30*

József Sándor

Full paper (PDF, 142 Kb) | Abstract

**Extensions to the Zeckendorf Triangle**

*Original research paper. Pages 31–34*

A. G. Shannon and J. V. Leyendekkers

Full paper (PDF, 83 Kb) | Abstract

**A combinatorial proof of multiple angle formulas involving Fibonacci and Lucas numbers**

*Original research paper. Pages 35–39*

Fernando Córes and Diego Marques

Full paper (PDF, 137 Kb) | Abstract

*F*and

_{n}*L*be the

_{n}*n*-th Fibonacci and Lucas number, respectively. In this note, we give a combinatorial proof for the following identity

**Conjectured polynomial time primality tests for numbers of special forms**

*Original research paper. Pages 40–43*

Predrag Terzić

Full paper (PDF, 145 Kb) | Abstract

*k*· 2

*− 1 are introduced.*

^{n}**Three identities concerning Fibonacci and Lucas numbers**

*Original research paper. Pages 44–48*

Refik Keskin

Full paper (PDF, 140 Kb) | Abstract

*z*

^{2}+

*x*

^{2}+

*y*

^{2}=

*xyz*+ 4.

**On the local and global principle for system of binary rational cubic forms**

*Original research paper. Pages 49–57*

Lan Nguyen

Full paper (PDF, 141 Kb) | Abstract

**On some Pascal’s like triangles. Part 7**

*Original research paper. Pages 58–63*

Krassimir T. Atanassov

Full paper (PDF, 159 Kb) | Abstract

**Identities involving q-Genocchi numbers and polynomials**

*Original research paper. Pages 64–74*

Serkan Aracı, Mehmet Acikgoz, Hassan Jolany and Yuan He

Full paper (PDF, 189 Kb) | Abstract

*q*-Genocchi numbers and polynomials. We introduce new identities of the

*q*-Genocchi numbers and polynomials by using the fermionic

*p*-adic integral on ℤ

*. Also, we give Cauchy-integral formula for the*

_{p}*q*-Genocchi polynomials and derive the distribution formula

*q*-Genocchi polynomials by using measure theory on

*p*-adic integral. Finally, we get

*q*-Zeta-type function by using Mellin transformation (sometimes known as Laplace transformation) and show that this function interpolates to the

*q*-Genocchi polynomials at negative integers.

**Volume 20** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4 ▷ Number 5