Posts Tagged ‘irreductibility’

## Irreductible polynomial with paired roots

April 11, 2011
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Suppose is an irreductible polynomial which has a complex root such that is also a root for . Prove that for any other root of , is also a root for .

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Categories: Algebra, Olympiad, Problem Solving
irreductibility, irreductible, polynomial

## Irreductible Polynomials Article AMM

March 26, 2010
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Let be a polynomial of degree in and set .

If is prime for some integer , then is irreductible in . Read more…

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AMM, irreductibility

## Irreductible polynomial

January 17, 2010
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Suppose is a polynomial with integer coefficients such that is an odd prime, and the roots of form a regular polygon in the complex plane. Prove that is irreductible in .

*Ioan Baetu, Romanian Mathematical Gazette*

Categories: Algebra, Olympiad, Problem Solving
irreductibility, irreductible, polynomial

## Position of roots

November 9, 2009
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The following result is quite useful in irreductibility problems for polynomials.

Prove that if then all the roots of satisfy or a root of unity of some order.

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Categories: Algebra, Complex analysis, Higher Algebra, Problem Solving
irreductibility, polynomial, roots