Number theory
$5,090 bountynobody has started
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
Even one lemma helps. Whoever finishes this later shares the pool with everyone who got them there.
contrib new erdos-124-erdos124-ne-zeroCommand line, then a pull request on GitHub.
Nothing has been published against this problem yet.
A first lemma is worth as much as a last one: whoever closes the problem shares the pool with everyone who got them there.
conjectures-tasks
The pinned statement, the Lean challenge file and the exact bundle you build against.
pool/tier-1/erdos-124-erdos124-ne-zero-formalized →
conjectures-contribution
Every published piece for this problem, with its Lean source and its signed record.
contributions/erdos-124-erdos124-ne-zero →
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«124»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos124.erdos124.ne_zero" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∀ (k : ℕ),
k ≠ 0 →
∀ (D : Finset ℕ),
(∀ d ∈ D, 3 ≤ d) →
1 ≤ ∑ d ∈ D, (↑d - 1)⁻¹ →
D.gcd id = 1 → ∀ᶠ (n : ℕ) in Filter.atTop, n ∈ ∑ d ∈ D, Erdos124.sumsOfDistinctPowers d kOriginal conjecture source: FormalConjectures/ErdosProblems/124.lean
References
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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