The board / number theory / #405
Erdős Problem #405
PROVED LEANdatabase updated 2026-08-24
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(p\) be an odd prime. Is it true that the equation \((p-1)!+a^{p-1}=p^k\) has only finitely many solutions? Originally proposed by Erdős and Graham [ErGr80]. Brindza and Erdős [BrEr91] proved that there are finitely many such solutions.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/405.Prizenone
Topicsnumber theory, factorials
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/405
Attempts
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