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

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

2010-05-10

arxiv.org/abs/1005.1533v1

Math. Comp. 80 (2011), 429-435

Mathematics

Number Theory

10 pages, to appear in Math. Comp

Scientific paper

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.

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