The number of steps in the Euclidean algorithm
Abstract
For all pairs of positive integers u, v with u <= v we define L(u, v) to be the number of steps required in applying the Euclidean algorithm to the pair u, v. Then given any [epsilon] > 0 there exists c0 > 0 such that for all except at most x2 exp{c0(log x)[epsilon]/2} of the pairs u, v with 1 <= u <= v <= x.
 Publication:

Journal of Number Theory
 Pub Date:
 November 1970
 DOI:
 10.1016/0022314X(70)900442
 Bibcode:
 1970JNT.....2..414D