On the greatest prime factor of (𝑎𝑏+1)(𝑎𝑐+1)

Corvaja, P.; Zannier, U.

doi:10.1090/S0002-9939-02-06771-0

On the greatest prime factor of $(ab+1)(ac+1)$
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by P. Corvaja and U. Zannier PDF

Proc. Amer. Math. Soc. 131 (2003), 1705-1709 Request permission

Abstract:

We prove that for integers $a>b>c>0$, the greatest prime factor of $(ab+1)(ac+1)$ tends to infinity with $a$. In particular, this settles a conjecture raised by Györy, Sarkozy and Stewart, predicting the same conclusion for the product $(ab+1)(ac+1)(bc+1)$.

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