Let F be a field and let e(x), g(x), h(x), and f(x) be polynomials in F[x] with h(x) of positive degree. Prove that if e(x) = gcd(g(x),h(x)) and e(x) divides f(x), then there is a polynomial j(x)in F[x] such that

g(x)j(x)=f(x)(modh(x)).

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- Nov 7th 2008, 08:58 AMwvlilgurlmodern alg
Let F be a field and let e(x), g(x), h(x), and f(x) be polynomials in F[x] with h(x) of positive degree. Prove that if e(x) = gcd(g(x),h(x)) and e(x) divides f(x), then there is a polynomial j(x)in F[x] such that

g(x)j(x)__=__f(x)(modh(x)). - Nov 7th 2008, 10:42 AMThePerfectHacker