# Prime divisors of sequences of integers

## TL;DR

This paper explores prime divisors in integer sequences, extending Furstenberg's proof of infinite primes and providing new proofs for classical results like Schur's theorem and properties of linear recurrence sequences.

## Contribution

It offers a simplified proof of the infinite prime divisors in non-degenerate linear recurrence sequences, building on Furstenberg's approach and advancing understanding of prime divisors in sequences.

## Key findings

- Proved that non-degenerate linear recurrence sequences have infinitely many prime divisors
- Extended Furstenberg's proof to a broader class of sequences
- Provided simplified proofs of classical results like Schur's theorem

## Abstract

In this paper, we develop Furstenberg's proof of infinity of primes, and prove several results about prime divisors of sequences of integers, including the celebrated Schur's theorem. In particular, we give a simple proof of a classical result which says that a non-degenerate linear recurrence sequence of integers of order k>1 has infinitely many prime divisors.