# Volume 10, 2004, Number 2

**Volume 10** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**Some properties of Fermatian numbers**

*Original research paper. Pages 25—33*

A. Shannon

Full paper (152 Kb) | Abstract

This paper looks at some basic number theoretic properties of Fermatian numbers. We define the

*n*-th reduced Fermatian number in terms of

so that 1_{n} = *n*, and 1_{n}! = *n*!, where *q*_{n}! = *q*_{n}q_{n−1}…*q*_{1}.

Some congruence properties and relationships with Bernoulli and Fibonacci numbers are explored. Some aspects of the notation and meaning of the Fermatian numbers are also outlined.

**On five Smarandache’s problems**

*Original research paper. Pages 34—53*

M. Vassilev-Missana and K. Atanassov

Full paper (5956 Kb)

**Some representations concerning the product of divisors of ***n*

*Original research paper. Pages 54—56*

M. Vassilev-Missana

Full paper (896 Kb) | Abstract

Let us denote by

*τ(n*) the number of all divisors of

*n*. It is well-known (see, e.g.,

) that

(1)

and of course, we have

(2)

But (1) is not a good formula for *P*_{d}(*n*), because it depends on function *τ* and to express *τ*(*n*) we need the prime number factorization of *n*.

Below, we give other representations of *P*_{d}(*n*) and *p*_{d}(*n*), which do not use the prime number factorization of *n*.

**Volume 10** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4