Mathematics Tripos Papers

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4.I.2C

Groups, Rings and Modules | Part IB, 2005

State Eisenstein's irreducibility criterion. Let nnn be an integer >1>1>1. Prove that 1+x+…+xn−11+x+\ldots+x^{n-1}1+x+…+xn−1 is irreducible in Z[x]\mathbb{Z}[x]Z[x] if and only if nnn is a prime number.

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