A note on Carlitz Wieferich primes
| dc.contributor.author | Bamunoba, Alex Samuel | |
| dc.date.accessioned | 2026-03-05T09:08:00Z | |
| dc.date.issued | 2017 | |
| dc.description.abstract | Abstract In 1994, D. Thakur introduced the notion of Wieferich primes for the Carlitz module, hereafter called c-Wieferich primes. At almost the same time, L. Denis proved the Carlitz module analogue of the famous Fermat’s Last Theorem. In this article, we relate Thakur’s definition of c-Wieferich primes to Denis’ result and state the necessary and sufficient condition for a monic irreducible (prime) polynomial Pin Fq[T]to be c-Wieferich. We use this condition to give another proof for infinitude of c-Wieferich primes in F2[T]and in addition construct two algorithms for computing c-Wieferich primes. With the help of the SAGE software, we compute several examples of c-Wieferich primes for the rings Fq[T], where q∈{3, 5, 7, 11, 13, 19, 29, 37}. Lastly, we unconditionally prove infinitude of non-c-Wieferichprimes in Fq[T]for q>2. | |
| dc.description.sponsorship | This work was carried out with financial support from the AIMS-DAAD Scholarship (A/13/90157), the University of Stellenbosch PostgraduateMerit Bursary Scheme, the Governmentof Canada’s International Development Research Centre (IDRC) Grant number107185-001, and within the framework of the AIMS Research for Africa Project. | |
| dc.identifier.citation | Bamunoba, A. S. (2017). A note on Carlitz Wieferich primes. Journal of Number Theory, 174, 343–357. https://doi.org/10.1016/j.jnt.2016.09.036 | |
| dc.identifier.uri | https://ir.lirauni.ac.ug/handle/123456789/1047 | |
| dc.language.iso | en | |
| dc.publisher | Journal of Number Theory | |
| dc.subject | The Carlitz module Carlitz polynomials and c-Wieferich primes | |
| dc.title | A note on Carlitz Wieferich primes | |
| dc.type | Article |