How smooth is \(\varphi(2^n+3)\)? (Q1767351)

If \(n\) is any integer, denote the largest prime divisor of \(n\) by \(P(n)\). The author proves that \(P(\varphi(2^n+3))\) tends to infinity with \(n\) on a set of \(n\) with asymptotic density \(1\), where \(\varphi(*)\) is Euler's totient. He also establishes a certain lower bound with respect to \(P(\varphi(| u_n|))\) where \((u_n)_{n\geq0}\) is a binary recurrent sequence of integers, but too technical to state here.