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?
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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
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Formal boundary
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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.