Number Theory

   

Elementary Proof that an Infinite Number of Pell Primes Exist

Authors: Stephen Marshall

This paper presents a complete proof of the Pell Primes are infinite. We use a proof found in Reference 1, that if p > 1 and d > 0 are integers, that p and p + d are both primes if and only if for integer m: m = (p-1)!( + ) + + We use this proof for d = - to prove the infinitude of Pell prime numbers. The author would like to give many thanks to the authors of 1001 Problems in Classical Number Theory, Jean-Marie De Koninck and Armel Mercier, 2004, Exercise Number 161 (see Reference 1). The proof provided in Exercise 6 is the key to making this paper on the Pell Prime Conjecture possible.

Comments: 15 Pages.

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Submission history

[v1] 2017-03-02 16:52:23

Unique-IP document downloads: 27 times

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