Volume 11, 2005, Number 3

Volume 11 ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

Remarks on compositions of numbers into relatively prime parts
Original research paper. Pages 1–6
H. W. Gould
Full paper (PDF, 73 Kb)

Infinite series and modular rings
Original research paper. Pages 7–14
J. V. Leyendekkers and A. G. Shannon
Full paper (PDF, 121 Kb) | Abstract

Thirteen convergent infinite series have been analysed in terms of modular rings. Thie enables one to assess the contribution of different categories of integers to the infinite series. One class of even integers contributes 1/6(π/4)2 to a zeta-function with exponent 2. Another class of even integers makes one quarter the contribution of all the integers to this series.

On the sum of equal powers of the first n terms of an arbitrary arithmetic progression. I
Original research paper. Pages 15–21
Peter Vassilev and Mladen Vassilev-Missana
Full paper (PDF, 2369 Kb)

On one remarkable identity involving Bernoulli numbers
Original research paper. Pages 22–24
Peter Vassilev and Mladen Vassilev-Missana
Full paper (PDF, 1079 Kb) | Abstract

In the present short note we propose and prove some new identities involving Bernoulli numbers and binomial coefficients. One of these identities is the main results of the paper.

Digit sum bases for Fibonacci and related numbers
Original research paper. Pages 25–32
Krassimir T. Atanassov and Anthony G. Shannon
Full paper (PDF, 2872 Kb) | Abstract

In [1–4] a digital arithmetical function is defined and its properties are described. Here we shall discuss its application to Fibonacci types of sequences.

Volume 11 ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

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