The board / number theory / #445
Erdős Problem #445
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).
The property that there exist \(a,b\in(n,n+p^c)\) such that \(ab\equiv 1\pmod{p}\).
Is it true that, for any \(c>1/2\), if \(p\) is a sufficiently large prime then, for any \(n\geq 0\), there exist \(a,b\in(n,n+p^c)\) such that \(ab\equiv 1\pmod{p}\)? This is discussed in this MathOverflow question [MathOverflow].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/445.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/445
Attempts
submit one →Search produced no proof claim. Open.
NO PROGRESS