Number theory
Date added
$5,226 bounty1 piece from 1 personlast one 2 months ago1 proof submitted, 3 months ago
A complete proof or refutation in Lean. The first one the validator accepts closes the problem and receives the bounty.
A lemma, a definition, a special case. There is no race: when someone closes the problem, up to half of its bounty can go to the recognised pieces that led there.
contrib new erdos-1003Command line, then a pull request on GitHub.
1 piece · 16 lemmas
2 Sept 2026
Erdős 1003: totient-collision counting API for phi(n)=phi(n+1) with finite reformulation
5FqLp5…FfZZiK · 16 lemmas
conjectures-tasks
The pinned statement, the Lean challenge file and the exact bundle you build against.
versions/fc-v2-erdos1003-erdos-1003-63d9c269e46a5e24f696c4f1-formalized →
conjectures-contribution
Every published piece for this problem, with its Lean source and its signed record.
contributions/erdos-1003 →
Formal statement
Proof target
import Mathlib
import FormalConjectures.ErdosProblems.«1003»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos1003.erdos_1003" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔ {n | n.totient = (n + 1).totient}.InfiniteOriginal conjecture source: FormalConjectures/ErdosProblems/1003.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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