Volume 5, 1999, Number 1

Volume 5 ▶ Number 1 ▷ Number 2Number 3Number 4

An analysis of Mersenne—Fibonacci and Mersenne—Lucas primes
Original research paper. Pages 1-26
J. V. Leyendekkers, J. M. Rybak and A. G. Shannon
Full paper (PDF, 1.3 Mb) | Abstract

Mersenne-Fibonacci primes, (2p − 1), (the classical Mersenne primes), and Mersenne-Lucas primes ((2p + l)/3), p a prime, are analysed within the framework of the modular ring ℤ4. These primes are restricted to Class 3 of ℤ4 and are composed of single-class “nests” of integers. The reason some p values do not give (2p − 1) as a prime is explained in terms of the two-parameter equation for composite integers given in a previous paper by the authors, the difference of squares, and Fermat’s “Little Theorem”. The Fermat characteristics are explored up to exponents of 257. The reasons for the terminology are given in the context that the two types of Mersenne primes are related to one another analogously to the way the Fibonacci and Lucas numbers are inter-related.

Corrigendum to Z6 & Pythagorean triangle area
Original research paper. Page 27
J. V. Leyendekkers, J. M. Rybak and A. G. Shannon
Full paper (PDF, 29 Kb)

A remark on the h1(τ)-function
Original research paper. Pages 28—32
J. Park
Full paper (PDF, 169 Kb)

On the 4-th Smarandache’s problem
Original research paper. Pages 33—35
K. Atanassov
Full paper (PDF, 97 Kb)

On the 16-th Smarandache’s problem
Original research paper. Pages 36—38
K. Atanassov
Full paper (PDF, 91 Kb)

On the 126-th Smarandache’s problem
Original research paper. Pages 39—40
K. Atanassov
Full paper (PDF, 58 Kb)


Volume 5 ▶ Number 1 ▷ Number 2Number 3Number 4

Comments are closed.