Can a prime p satisfy 2 p − 1 ≡ 1 ( mod p 2 ) {\displaystyle 2^{p-1}\equiv 1{\pmod {p^{2}}}} {\displaystyle 2^{p-1}\equiv 1{\pmod
Source placement record
Can a prime p satisfy 2 p − 1 ≡ 1 ( mod p 2 ) {\displaystyle 2^{p-1}\equiv 1{\pmod {p^{2}}}} {\displaystyle 2^{p-1}\equiv 1{\pmod {p^{2}}}} and 3 p − 1 ≡ 1 ( mod p 2 ) {\displaystyle 3^{p-1}\equiv 1{\pmod {p^{2}}}} {\displaystyle 3^{p-1}\equiv 1{\pmod {p^{2}}}} simultaneously?
Here is what the pinned source says, where it came from, and what still needs editorial review.
Source status
Open
Field
Number theory · Prime numbers
Record type
Revision-pinned source placement
Verification
Source-index reviewed
Source grade
secondary
Reviewed
2026-07-27T18:04:33.834Z
Context and review boundary
The source list does not provide a uniform standalone exposition for every row. Use the exact subsection and linked topic article as the starting point for a reviewed reading trail.
Formal boundary
No independent formal statement has been added to this source-index record. This prevents the catalog from inventing notation or silently strengthening the cited claim.
Known approaches and partial results
Pending review. No structured approach or partial-result note has been added to this source placement.
Source trail
Wikipedia list subsection — Exact Number theory › Prime numbers subsection in the revision-pinned source.