irreducible polynomials obtained from biquadratic fields


Let m and n be distinct squarefreeMathworldPlanetmath integers, neither of which is equal to 1. Then the polynomialPlanetmathPlanetmath


is irreducible ( (over Q).


By the theorem stated in the parent entry (, m+n is an algebraic numberMathworldPlanetmath of degree ( 4. Thus, a polynomial of degree 4 that has m+n as a root must be over . We set out to construct such a polynomial.


Title irreducible polynomials obtained from biquadratic fields
Canonical name IrreduciblePolynomialsObtainedFromBiquadraticFields
Date of creation 2013-03-22 17:54:22
Last modified on 2013-03-22 17:54:22
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 5
Author Wkbj79 (1863)
Entry type Corollary
Classification msc 12F05
Classification msc 12E05
Classification msc 11R16
Related topic ExamplesOfMinimalPolynomials
Related topic BiquadraticEquation2