Primes in a prescribed arithmetic progression dividing the sequence a^k+b^k

Details Primes in a prescribed arithmetic progression dividing the sequence a^k+b^k Primes in a prescribed arithmetic progression dividing the sequence a^k+b^k

2007-03-30

arxiv.org/abs/math/0703925v1

Mathematics

Number Theory

22 pages, 13 tables

Scientific paper

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.

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