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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
$4,761
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.
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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:df15e62f90696db32e1207a0e13eeaf87199ce238a736ac97ac633b72f86576f
Task id fc-379fc029-erdos249-erdos-249-8223256295-counterexample-v1
Task commitment sha256:4faeaca69456ff1b3e951860e26a10d75b7d33b06d0df89fc1a89026159c1469 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.
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Erdős problem 249 · Conjectures.io