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arXiv · 1005.1533

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

Florian Luca·Filip Najman
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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.

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Florian Luca, Filip Najman. 2010-05-10. On the largest prime factor of $x^2-1$. https://arxiv.org/abs/1005.1533

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