Volume 11, 2005, Number 2

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

The sum-of-divisors minimum and maximum functions
Original research paper. Pages 1—8
József Sándor
Full paper (PDF, 176 Kb)

Note on some identities related to binomial coefficients
Original research paper. Pages 9—12
Mladen V. Vassilev-Missana
Full paper (PDF, 1191 Kb)

Fermat’s theorem on binary powers
Original research paper. Pages 13—22
J. Leyendekkers and A. Shannon
Full paper (PDF, 118 Kb) | Abstract

Modular rings are used to analyse integers of the form N = 2m + 1. When m is odd, the integer structure prevents the formation of primes. When m is even, N ‘commonly’ has a right-end-digit of 5 and so is not a prime then. However, a sequence defined by m = 4 + 4q, q = 0, 1, 2, 3 can generate some primes as the right-end-digit is 7. Elements of this sequence satisfy the non-linear recurrence relation Gm = Gm−12 − 2Gm−1 + 2. Fermat numbers, where m = 2n satisfy this recurrence relation. However, in this case, the integer structure reveals that primes are limited to n < 5.

The birthday inequality
Original research paper. Pages 23—24
Krassimir T. Atanassov
Full paper (PDF, 528 Kb)

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

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