On the largest prime factor of $x^2-1$

Florian Luca; Filip Najman

On the largest prime factor of $x^2-1$

Number Theory 2011-11-24 v1

Authors: Florian Luca , Filip Najman

Abstract

In this paper, we find all integers $x$ such that $x^{2}-1$ has only prime factors smaller than 100. This gives some interesting numerical corollaries. For example, for any positive integer $n$ we can find the largest positive integer $x$ such that all prime factors of each of $x, x+1,..., x+n$ are less than 100.

Keywords

largest prime factor smooth numbers integer solutions numerical corollaries consecutive integers

Cite

@article{arxiv.1005.1533,
  title  = {On the largest prime factor of $x^2-1$},
  author = {Florian Luca and Filip Najman},
  journal= {arXiv preprint arXiv:1005.1533},
  year   = {2011}
}

Comments

10 pages, to appear in Math. Comp

On the largest prime factor of $x^2-1$

Abstract

Keywords

Cite

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