Home > RHUMJ > Vol. 9 (2008) > Iss. 2

#### Article Title

#### Abstract

A generalized Sierpinski number base b is an integer k>1 for which gcd(k+1,b-1)=1, k is not a rational power of b, and kbn+1 is composite for all n>0. Given an integer k>0, we will seek a base b for which k is a generalized Sierpinski number base b. We will show that this is not possible if k is a Mersenne number. We will give an algorithm which will work for all other k provided that there exists a composite in the sequence {(k2m+1)/gcd(k+1,2)} for m ≥ 0.

#### Sponsor

Chris Caldwell, Mathematics and Statistics, The University of Tennessee at Martin caldwell@utm.edu

#### Recommended Citation

Krywaruczenko, Daniel
(2008)
"A Reverse Sierpinski Number Problem,"
*Rose-Hulman Undergraduate Mathematics Journal*: Vol. 9
:
Iss.
2
, Article 4.

Available at:
http://scholar.rose-hulman.edu/rhumj/vol9/iss2/4