OPEN

How large is the largest prime factor of $n(n+1)$?

Mahler

[Ma35] showed that this is $\gg \log\log n$. Schinzel

[Sc67b] observed that for infinitely many $n$ it is $\leq n^{O(1/\log\log\log n)}$. The truth is probably $\gg (\log n)^2$ for all $n$.