Let F be a field, and let f(x) and g(x) belong to F[x]. If
Chapter 16, Problem 45E(choose chapter or problem)
Problem 45E
Let F be a field, and let f(x) and g(x) belong to F[x]. If there is no polynomial of positive degree in F[x] that divides both f(x) and g(x) [in this case, f(x) and g(x) are said to be relatively prime], prove that there exist polynomials h(x) and k(x) in F[x] with the property that f(x)h(x) + g(x)k(x) = 1. (This exercise is referred to in Chapter 20.)
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