Problem Statement
Let $t>1$ be a rational number. Is\[\sum_{n=1}^\infty\frac{1}{t^n-1}=\sum_{n=1}^\infty \frac{\tau(n)}{t^n}\]irrational, where $\tau(n)$ counts the divisors of $n$?
Categories:
Irrationality
Progress
A conjecture of Chowla. Erdős [Er48] proved that this is true if $t\geq 2$ is an integer.Source: erdosproblems.com/1049 | Last verified: January 19, 2026