**Volume 15** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**On the Euler minimum and maximum functions**

*Original research paper. Pages 1—8*

József Sándor

Full paper (PDF, 115 Kb)

**On the monotonicity of the sequence** (*σ _{k} / σ*_{k}*)

*Original research paper. Pages 9—13*

József Sándor

Full paper (PDF, 157 Kb) | Abstract

*k*-th powers of divisors, resp. unitary divisors of a number, is decreasing upon

*k*.

**The integer structure of the difference of two odd-powered odd integers**

*Original research paper. Pages 14—20*

J. V. Leyendekkers and A. G. Shannon

Full paper (PDF, 163 Kb) | Abstract

*Z*

_{4}was used to analyse the structure of the integer,

*N*, obtained from

*x*,

^{n}− y^{n}*x*,

*y*,

*n*odd. The constraints on

*x*and

*y*associated with the probability of

*x*(

^{n}− y^{n}= N = z^{n}*z*even) were explored. When

*n*∈ ̅3

_{4}(

*n*= 3, 7, 11, 15, …) the structure of

*N*is 4

*r*

_{0}(4

*r*

_{3}+ 3) that is ̅0

_{4}× ̅3

_{4}. When

*n*∈ ̅1

_{4}(

*n*= 5, 9, 13, 17, …) the structure of

*N*is 4

*r*

_{0}(4

*r*

_{1}+ 1) that is ̅0

_{4}× ̅1

_{4}. The row structures and right-end-digit patterns of the rows of (

*x*

^{3}−

*y*

^{3}) and

*z*

^{3}were compared and shown to be incompatible, as expected.

**A remark on an arithmetic function. Part 2**

*Original research paper. Pages 21—22*

Krassimir Atanassov

Full paper (PDF, 87 Kb)

** A problem related to Fibonacci-like type sequences**

*Original research paper. Pages 23—24*

Mladen Vassilev-Missana

Full paper (PDF, 95 Kb)