The board / number theory / #479
Erdős Problem #479
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Is it true that, for every integer \(k\neq 1\), there are infinitely many \(n\) such that \(2^n\equiv k\pmod{n}\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/479.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/479
Attempts
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Proved an exact classification for all solutions with at most one odd prime divisor, verified explicit extension certificates, and exhaustively enumerated \(n\leq20{,}000{,}000\) for \(|k|\leq20\); th
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