Erdős problem 1049 · problems.science

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 $n$ ?

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FormalConjectures/ErdosProblems/

1049.lean

Retained formal statement2 of 3

Erdős [Er48] proved that this is true if $t\geq 2$ is an integer.

FormalConjectures/ErdosProblems/1049.leanErdos1049.erdos_1049.variants.geq_2_integer1 lineExact file

1∀ t ≥ 2, Irrational (∑' (n : ℕ+), 1 / (↑t ^ ↑n - 1))

SolvedStatement only, no proof

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