Volume 15, 2009, Number 3

Volume 15Number 1Number 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 (σk / σ*k)
Original research paper. Pages 9—13
József Sándor
Full paper (PDF, 157 Kb) | Abstract

We prove that the sequence of ratios of the 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

The modular ring Z4 was used to analyse the structure of the integer, N, obtained from xn − yn, x, y, n odd. The constraints on x and y associated with the probability of xn − yn = N = zn (z even) were explored. When n ∈ ̅34 (n = 3, 7, 11, 15, …) the structure of N is 4r0(4r3 + 3) that is ̅04 × ̅34. When n ∈ ̅14 (n = 5, 9, 13, 17, …) the structure of N is 4r0(4r1 + 1) that is ̅04 × ̅14. The row structures and right-end-digit patterns of the rows of (x3y3) and z3 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)


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

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