A Reverse Sierpinski Number Problem

Authors

Daniel Krywaruczenko, University of Tennessee at MartinFollow

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.

Author Bio

Dan is originally from Chicago Illinois. For most of his undergraduate career he was on a sports scholarship as a football player. He wrote this paper while finishing his mathematics degree at the University of Tennessee at Martin and is now beginning a Masters in Statistics at Mississippi State University. After this Masters, Dan hopes to continue his education with a second Masters in Engineering Management. Dan uses the competitiveness and team attitudes that he learned in football while continuing in academia.

Faculty Sponsor

Chris Caldwell

Recommended Citation

Krywaruczenko, Daniel (2008) "A Reverse Sierpinski Number Problem," Rose-Hulman Undergraduate Mathematics Journal: Vol. 9: Iss. 2, Article 4.
Available at: https://scholar.rose-hulman.edu/rhumj/vol9/iss2/4