Algebraic integers may be the roots of nonmonic primitive polynomials

Show that an algebraic integer may be expressed as a root of a nonmonic primitive polynomial.


Certainly the roots of x^2+1 are algebraic integers (namely, \pm i). Consider (x^2+1)(2x+3) = 2x^3 + 3x^2 + 2x + 3; this polynomial is primitive and nonmonic, and has \pm i as roots.

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