Problem Statement
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?
Categories:
Number Theory
Progress
Erdős [Er95] could prove the distribution function is purely singular.Source: erdosproblems.com/50 | Last verified: January 13, 2026