Kunze Linear Algebra · Problem 4.5.2

Polynomials

Mathematics — Methods · gcd-common-roots-complex

Problem

Assuming the Fundamental Theorem of Algebra, prove the following. If

f

and

g

are polynomials over the field of complex numbers, then

\gcd(f, g) = 1

if and only if

f

and

g

have no common root.