16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 4.5.2

Polynomials

Mathematics — Linear Algebra · gcd-common-roots

Problem

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

f

and

g

are polynomials over the field of complex numbers, then

\mathrm{g.c.d.}(f,g) = 1

if and only if

f

and

g

have no common root.