Problem 50

Erdős Problem #50: declared status 'open'. Formalized: yes. Schoenberg proved that for every $c\in [0,1]$ the density of$$\{ n\in \mathbb{N} : \phi(n)<cn\}$$exists. Let this density be denoted by $f(c)$. Is it true that there are no $x$ such that $f'(x)$ exists and is positive? Prize: $250. Tags: number theory.