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For given f1,..., fm ∈ K[x] that are relatively prime, where K is a field, Kalkbrener, Sweedler, and Taylor (1993) present degree bounds on the ai needed to express 1 (and other low degree polynomials) as Σaifi. Their bounds are an improvement on bounds given by Kakié (1976). This note presents a direct proof of the following fact.

Direct proof of a theorem by Kalkbrener, Sweedler, and Taylor