Primes in a prescribed arithmetic progression dividing the sequence a^k+b^k
Number Theory
2012-07-30 v1
Abstract
Given positive integers a,b,c and d such that c and d are coprime we show that the primes p=c(mod d)dividing a^k+b^k for some k>=1 have a natural density and explicitly compute this density. We demonstrate our results by considering some claims of Fermat that he made in a 1641 letter to Mersenne.
Cite
@article{arxiv.math/0703925,
title = {Primes in a prescribed arithmetic progression dividing the sequence a^k+b^k},
author = {P. Moree and B. Sury},
journal= {arXiv preprint arXiv:math/0703925},
year = {2012}
}
Comments
22 pages, 13 tables