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

**On certain inequalities involving Dedekind’s arithmetical function**

*Original research paper. Pages 1–4*

József Sándor

Full paper (PDF, 148 Kb)

**Remark on φ and ψ functions**

*Original research paper. Pages 5–6*

Krassimir T. Atanassov

Full paper (PDF, 93 Kb)

**Two asymptotic formulas related to bi-unitary divisors**

*Original research paper. Pages 7–14*

Antal Bege

Full paper (PDF, 189 Kb)

**More explanations about Baica’s proof of Fermat’s last theorem**

*Original research paper. Pages 15–19*

Malvina Baica

Full paper (PDF, 219 Kb) | Abstract

*In this paper the author will answer some questions raised at some various professional conferences and meetings when she presented her proof [1] of Fermat’s Last Theorem.*

**The Euclidean character of the Fermat’s last theorem**

*Original research paper. Pages 20–23*

Malvina Baica

Full paper (PDF, 225 Kb) | Abstract

In this paper the author is expressing her genuine concern about the proof of

Fermat’s Last Theorem in the Geometry of the Elliptic Curves or Elliptic Variety

which may not be equivalent to the result in the Euclidean Geometry or Euclidean

Variety, where Fermat’s Last Theorem was initially originated, about three hundred

fifty years ago.

In this paper the author is expressing her genuine concern about the proof of

Fermat’s Last Theorem in the Geometry of the Elliptic Curves or Elliptic Variety

which may not be equivalent to the result in the Euclidean Geometry or Euclidean

Variety, where Fermat’s Last Theorem was initially originated, about three hundred

fifty years ago.

**On two arithmetic sets**

*Original research paper. Pages 24–27*

Krassimir Atanassov and Mladen Vassilev-Missana

Full paper (PDF, 160 Kb)

**Note on some classical arithmetic functions**

*Original research paper. Pages 28–32*

Mladen V. Vassilev-Missana

Full paper (PDF, 214 Kb)

**The anatomy of even exponent Pythagorean triples**

*Original research paper. Pages 33–52*

J. V. Leyendekkers, J. M. Rybak and A. G. Shannon

Full paper (PDF, 579 Kb) | Abstract

*This paper uses a novel approach to analyse the diophantine equation d2n = e2n + f 2n in a number of ways for even and odd n, and with the use of the equivalence classes of the modular ring ℤ*

of primitive Pythagorean triples and right-most digit patterns.

_{6}, the characteristicsof primitive Pythagorean triples and right-most digit patterns.

**The Goldbach problem (II)**

*Original research paper. Pages 53–68*

Aldo Peretti

Full paper (PDF, 596 Kb) | Abstract

*p*such that . Are proed formulas (14) and(26), which express its value in terms of Chebyshev’s function In this way is obtained formula (38), that gives the asymptotic value of

_{i}*s(t)*with a new ”singular” series which runs through the zeros of the Zeta function, but that at present can not be evaluated in a sufficiently accurate form. In second place, for the function (with ), already considered by Hardy-Littlewood in ”Partitio Numerorum III” (P.N.III), is proved the exact formula

- where second difference;

- and are the direct and inverse Laplace transforms;

The circle method applied in P.N.III is equivalent to determine through the comlpex inversion formula along a Bromwich contour. But it is evident that is much preferable to employ tables of direct and inverse transforms because the functions involved are elementary; because is obtained an exact expression for the remainder, and because all the calculus is by far more simple.One arrive thus to the inconditional formula (130), which very closely resembles the famous conjecture A of P.N.III.