The exact length of the Euclidean algorithm in [ X ]
Arnold Knopfmacher, John Knopfmacher · Mathematika · 1988
A study is made of the length L(h, k) of the Euclidean algorithm for determining the g.c.d. of two polynomials h, k in [X], a finite field. We obtain exact formulae for the number of pairs with a fixed length N which lie in a given range, as well as the average length and variance of the Euclidean algorithm for such pairs.