Cohn's irreducibility criterion is a sufficient condition for determining that a polynomial with integer coefficients cannot be factored into a product of lower-degree polynomials with integer coefficients. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementIf a prime number p is expressed in base 10 as p = a_m 10^m + a_{m-1} 10^{m-1} + ... + a_1 10 + a_0 with 0 less than or equal to a_i less than or equal to 9, then the polynomial f(x) = a_m x^m + ... + a_0 is irreducible in Z[x]. 1 Classification
Statement Form Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Cohn's irreducibility criterion (Wikipedia)
IntroductionQuote, Introduction
then the polynomial f(x) = a_m x^m + a_{m-1} x^{m-1} + ? + a_1 x + a_0 is irreducible in Z[x]
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