Prove: let F be a field and let g(x) and h(x) be polynomials in F[x] with gcd(g(x),h(x))=1. Let a, b be elements of F with a‡b. Then gcd(h(x)-ag(x), h(x)-bg(x))=1.

Printable View

- March 2nd 2010, 06:54 PMapple2009great common divisor
Prove: let F be a field and let g(x) and h(x) be polynomials in F[x] with gcd(g(x),h(x))=1. Let a, b be elements of F with a‡b. Then gcd(h(x)-ag(x), h(x)-bg(x))=1.

- March 3rd 2010, 08:40 AMhatsoff