Viewing topic: Eisenstein Criterion

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Eisenstein Criterion

  • Definition: Let f(x)=(a_n)(x^n)+...+a_0 be an integer polynomial and let p be a prime integer. Suppose that the coefficients of f satisfy the following conditions: a) p does not divide a_n; b) p divides all other coefficients a_(n-1),...,a_0; and c) p^2 does not divide a_0. Then f is an irreducible element of Q[x].

    Source: Algebra, second edition by Michael Artin

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