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This paper presents an elementary treatment of the theory of subresultants, and examines the relationship of the subresultants of a given pair of polynomials to their polynomial remainder sequence as determined by Euclid's algorithm. Two important versions of Euclid's algorithm are discussed. The results are essentially the same as those of Collins, but the presentation is briefer, simpler, and somewhat more general.
Brown et al. (1971) studied this question.