MathDB
Q 5

Source:

May 25, 2007
algebrapolynomialinductionPolynomials

Problem Statement

(Eisentein's Criterion) Let f(x)=anxn+⋯+a1x+a0f(x)=a_{n}x^{n} +\cdots +a_{1}x+a_{0} be a nonconstant polynomial with integer coefficients. If there is a prime pp such that pp divides each of a0a_{0}, a1a_{1}, ⋯\cdots,an−1a_{n-1} but pp does not divide ana_{n} and p2p^2 does not divide a0a_{0}, then f(x)f(x) is irreducible in Q[x]\mathbb{Q}[x].
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