Common divisors of totients of polynomial sequences

 

Let $f$ be a primitive polynomial of degree $k$ in $\mathbb{Z}[x]$. Venkataramana studied common divisors of totients of $f(n)$ as $n$ varies over non-negative integers. He posed the question of finding a uniform bound on this quantity as we vary over primitive polynomials $f$ of degree $k$, depending only on $k$. In this talk, we will discuss some results in this direction. If time permits, we will report on a work in progress with Jean-Marc Deshouillers, Sanoli Gun and Papiya Sur.