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Erdős problem 672 Can the product of an arithmetic progression of positive integers n , n + d , . . . , n + ( k − 1 ) d n, n + d, ..., n + (k - 1)d n , n + d , ... , n + ( k − 1 ) d
of length ≥ 4, with ( n , d ) = 1 (n, d) = 1 ( n , d ) = 1 , be a perfect power?
$2,232 bounty · nobody has started
week of 28 Sept 2025 · nothing published week of 5 Oct 2025 · nothing published week of 12 Oct 2025 · nothing published week of 19 Oct 2025 · nothing published week of 26 Oct 2025 · nothing published week of 2 Nov 2025 · nothing published
Solve it Nobody has attempted this. A complete proof or refutation takes the whole bounty.
Add the first piece Even one lemma helps. Whoever finishes this later shares the pool with everyone who got them there.
Command line, then a pull request on GitHub.
← Erdős problem 653 Erdős problem 677 →
What has been built 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.
Proof target
import FormalConjectures.ErdosProblems.«672»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos672.erdos_672" := by
sorry
end Bounty
Open this target’s Challenge.lean Original conjecture (Lean type)
True ↔ ∀ (k l : ℕ), l > 1 → k ≥ 4 → Erdos672.Erdos672With k lOriginal conjecture source: FormalConjectures/ErdosProblems/672.lean
Source type SHA-256 sha256:c445617cb40577954b07647947103591146b81f79e29b214a02745fc58e09a1a
Task id fc-8432eac9-erdos672-erdos-672-713e8186eb-formalized-v1
Task commitment sha256:9319c919b34ffc4e079f87512387799fde189e458faa517513b0d7ae0d13bc04 week of 9 Nov 2025 · nothing published
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28 Sept 2025 nothing published against this one yet 20 Sept 2026
erdosproblems.com/672
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.
Our channel is in the Bittensor Discord server. Join the server first, then open the channel to send your report.
Reward
$2,232
for closing this problem
Whoever closes it takes the bounty. Published pieces that helped get there share a separate contribution pool, paid out once the problem is closed.
Set by bounty policy linear-age-v3-locked: 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.
Prove it or break it
The same problem accepts both. You can submit a proof of the statement or a counterexample that refutes it, and you choose which when you submit.
Prove the statement no attempts
Find a counterexample no attempts
Erdős problem 672 · Conjectures.io