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

*q*-Bernoulli numbers and polynomials via an invariant *p*-adic *q*-integral in Z_{p}

*Original research paper. Pages 105–110*

H.-K. Pak and S.-H. Rim

Full paper (PDF, 87 Kb) | Abstract

*q*-Bernoulli numbers by using an

*p*-adic

*q*-integral due to T. Kim and investigate the properties of these numbers. In the final section, we will give the formula for sums of products of these numbers.

**Intervals containing prime numbers**

*Original research paper. Pages 111–114*

L. Panaitopol

Full paper (PDF, 122 Kb) | Abstract

*x*> 0, let

*π(x)*be the number of prime numbers not exceeding

*x*. One shows that, for

*x ≥ 7*, there exists at least one prime number between

*x*and

*x + π(x)*, thus obtaining a result that is sharper than the one postulated by Bertrand.

**The analysis of twin primes within Z _{6}**

*Original research paper. Pages 115–124*

J. Leyendekkers and A. Shannon

Full paper (PDF, 490 Kb) | Abstract

_{6}defines integers via (6

*r*

**+ (**

_{i}*i*– 3)) where i is the Class and r, the row when tabulated in an array. Since only Classes 2

**and**

_{6}*4*

**(; contain odd primes, this modular ring is ideally suited for the analysis of twin primes. In considering a series of integers, a simple method is used to calculate rows (F rows) that do not contain twin primes. This allows the distribution of other primes to be found. Then, in considering the corresponding array of rows, elimination of the**

_{6 }*F*rows yields the rows which contain twin primes. The calculations are facilitated by the use of the right-end digit (RED) technique.

**Some properties of modified Lah numbers**

*Original research paper. Pages 125–131*

A. Shannon

Full paper (PDF, 180 Kb) | Abstract

**How Fermat’s Great Theorem helps solving the Diophantine equation
12. x^{3} − φ(y).y^{2} = 3.(φ(y))^{3}**

*Original research paper. Pages 132–134*

M. Vassilev-Missana

Full paper (PDF, 102 Kb)

**On one Jacobsthal’s inequality**

*Original research paper. Pages 135–136*

K. Atanassov

Full paper (PDF, 45 Kb)