**Volume 7** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**Some explicit formulae for the composite numbers**

*Original research paper. Pages 29—31*

Mladen Vassilev-Missana

Full paper (PDF, 256 Kb) | Abstract

*n*-th term of the sequence of all composite numbers and for the sequence of all off composite numbers are proposed.

**A note on the values of Zeta**

*Original research paper. Pages 32—35*

Taekyun Kim and Seog-Hoon Rim

Full paper (PDF, 432 Kb) | Abstract

*q*-calculation, we construct a

*q*-analogue of Riemann ζ-function, Hurwitz’s zeta function and prove some formulas for the values of these functions. By using these formulae, we can evaluate the values of ζ(5) −

*A*ζ(5, ¼) where

*A*is some rational number.

**On Heron triangles, III**

*Original research paper. Pages 36—47*

József Sándor

Full paper (PDF, 1376 Kb)

**Expansion of integer powers from Fibonacci’s odd number triangle**

*Original research paper. Pages 48—59*

J. V. Leyendekkers and A. G. Shannon

Full paper (PDF, 1495 Kb) | Abstract

_{4}is developed. This provides constraints for the various functions which help in solving polynomial and Diophantine equations, some simple examples of which are given.

**An elementary extension of Hermite’s equality**

*Original research paper. Page 60*

Krassimir T. Atanassov

Full paper (PDF, 96 Kb) | Abstract

*x*and each natural number

*n*

.

We shall extend it, proving that for each positive real number

*x*and each natural numbers

*k*and

*n*

.

**On 28-th Smarandache’s problem**

*Original research paper. Pages 61—64*

Mladen V. Vassilev-Missana and Krassimir T. Atanassov

Full paper (PDF, 469 Kb)