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

*N*= 2

*+ 1. When*

^{m}*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 + 4

*q*,

*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

*G*=

_{m}*G*

_{m−1}

^{2}− 2

*G*

_{m−1}+ 2. Fermat numbers, where

*m*= 2

*satisfy this recurrence relation. However, in this case, the integer structure reveals that primes are limited to*

^{n}*n*< 5.

**The birthday inequality**

*Original research paper. Pages 23—24*

Krassimir T. Atanassov

Full paper (PDF, 528 Kb)