cohn’s irreducibility criterion · polynomials are to irreducible polynomials as integers are to...

Nesbitt Room Cohn’s Irreducibility Criterion Carsten Peterson Abstract for 15 March Polynomials are to irreducible polynomials as integers are to prime numbers. Discussion of irreducible polynomials is often limited to algebra class, and the techniques learned for proving irreducibility are usually purely algebraic. In this talk we shall prove Cohn's irreducibility criterion which tells you that if you take your favorite prime number, p, and write it in your favorite base, b, as = ! !!! ⋯ ! , then the polynomial ! ! + ⋯ + ! is irreducible over the integers. The proof is entirely elementary and analytic in nature.

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Nesbitt Room

Cohn’s Irreducibility Criterion

Carsten Peterson

Abstract for 15 March

Polynomials are to irreducible polynomials as integers are to prime numbers. Discussion of irreducible polynomials is often limited to algebra class, and the techniques learned for proving irreducibility are usually purely algebraic. In this talk we shall prove Cohn's irreducibility criterion which tells you that if you take your favorite prime number, p, and write it in your favorite base, b, as 𝑝 =𝑏!𝑏!!!⋯ 𝑏!, then the polynomial 𝑏!𝑥! +⋯+ 𝑏! is irreducible over the integers. The proof is entirely elementary and analytic in nature.

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