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Bound on the complex roots of an irreducible monic polynomial.

Source: STEMS 2022 Math Cat A P1

January 24, 2022

algebrapolynomial

Problem Statement

Let

f

be an irreducible monic polynomial with integer coefficients such that

f(0)

is not equal to

1

. Let

z

be a complex number that is a root of

f

. Show that if

w

is another complex root of

f

, then

\frac{z}{w}

cannot be a positive integer greater than

1