  Let u(n) be the n-th term of a Lucas sequence or a Lehmer sequence.In this
article we shall establish an estimate from below for the greatest prime factor
of u(n) which is of the form nexp(logn/104loglogn). In so doing we are able to
resolve a question of Schinzel from 1962 and a conjecture of Erdos from 1965.In
addition we are able to give the first general improvement on results of Bang
from 1886 and Carmichael from 1912.
