I was reading this paper. There is a Lemma 1 saying that for a fixed prime $q$ the cardinality of the set $\{p \leq x \mid (\frac{q}{p})=-1\}$ such that all odd prime divisors of $p-1$ are greater than $x^{\frac{1}{4}-\epsilon}$, is at least $\frac{cx}{\log^2x}$ where $c>0$ is some constant.
Its written in one of the cited source that it follows from Theorem 1 of Rosser Seieve paper by Iwaneic (citation is mentioned in the original paper). But I don't understand how to do that. Could anyone please work out details for me ?