To prove: That every nonzero remainder r j ( x ) in the Euclidean Algorithm is a linear combination of f ( x ) and g ( x ) : r j ( x ) = f ( x ) s j ( x ) + g ( x ) t j ( x ) for some s j ( x ) and t j ( x ) in F [ x ] .

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Chapter 8.2, Problem 32E

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To prove: That every nonzero remainder rj(x) in the Euclidean Algorithm is a linear combination of f(x) and g(x): rj(x)=f(x)sj(x)+g(x)tj(x) for some sj(x) and tj(x) in F[x].

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