On the largest prime factor of 𝑥²-1

Luca, Florian; Najman, Filip

doi:10.1090/S0025-5718-2010-02381-6

On the largest prime factor of $x^2-1$
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by Florian Luca and Filip Najman PDF

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

Erratum: Math. Comp. 83 (2014), 337-337.
Table supplement: supplement

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 $x, x+1,\ldots , x+n$ are less than 100.

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