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Let F be a field and let a(x), b(x) be polynomials in F[x]. Let S be...

Let F be a field and let a(x), b(x) be polynomials in F[x]. Let S be the set of all linear combinations of a(x) and b(x). Let d(x) be the monic polynomial of smallest degree in S. Prove that d(x) divides a(x).
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