Catalog
Every problem here was open when it entered the pool. Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
A proof outlives the network that paid for it.
Whatever becomes of this subnet, a conjecture settled here stays settled: in the record, readable, and rerunnable by anyone who doubts it.
Erdős problem 249 Is
∑ n ϕ ( n ) 2 n \sum_{n} \frac{\phi(n)}{2^n} n ∑ 2 n ϕ ( n )
irrational? Here ϕ \phi ϕ is the Euler totient function.
Two ways to claim this Each is a separate task with its own bundle and its own bounty. Pick the one your proof argues for.
Bounty
$4,732
paid on an accepted proof
Set by bounty policy dynamic-age-v1: the amount is worked out from how long the problem has stood open, so it moves as the pool and the pool's age profile move.
Submit a proof Your file is checked for free before any credit is spent.
Lean type
True ↔ Irrational (∑' (n : ℕ), ↑n.totient / 2 ^ n)What you must prove
import FormalConjectures.ErdosProblems.«249»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos249.erdos_249" := by
sorry
end Bounty
Pinned source: FormalConjectures/ErdosProblems/249.lean
Source type SHA-256 sha256:50958c75eb82dfa63690899d9c7a87adaf9c4c6dc67de73e9782172842b2fe4d
Task id fc-379fc029-erdos249-erdos-249-db6e2417ae-formalized-v1
Task commitment sha256:a806efd018a3ba0535a1c9f79519a3a617bb9bf480bfebceb69d3e0c424756bf Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
Tell us on Discord
Erdős problem 249 · Conjectures.io