Agrawal's conjecture

Source placement record

Agrawal's conjecture that given coprime positive integers n {\displaystyle n} {\displaystyle n} and r {\displaystyle r} {\displaystyle r}, if ( X − 1 ) n ≡ X n − 1 ( mod n , X r − 1 ) {\displaystyle (X-1)^{n}\equiv X^{n}-1{\pmod {n,X^{r}-1}}} {\displaystyle (X-1)^{n}\equiv X^{n}-1{\pmod {n,X^{r}-1}}}, then either n {\displaystyle n} {\displaystyle n} is prime or n 2 ≡ 1 ( mod r ) {\displaystyle n^{2}\equiv 1{\pmod {r}}} {\displaystyle n^{2}\equiv 1{\pmod {r}}}

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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

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Source trail

Wikipedia list subsection — Exact Number theory › Prime numbers subsection in the revision-pinned source.
Wikipedia topic article — Background article linked by the source index; follow its references for deeper study.
Pinned source revision 1366281547 — Revision-pinned snapshot from 7/27/2026.