Euclid's algorithm is an ancient and efficient method for finding the GCD of two numbers. The algorithm is based on the observation that the GCD of two numbers does not change if the smaller number is ...

Abstract: The story behind the Euclidean algorithm and its relationship to the solution of the Diophantine equation is examined in this article. The Euclidean algorithm appears in Proposition 2 in ...

Mathematics of Computation, Vol. 77, No. 261 (Jan., 2008), pp. 589-607 (19 pages) We describe a new subquadratic left-to-right GCD algorithm, inspired by Schönhage's algorithm for reduction of binary ...

The PSLQ procedure can be regarded as a jazzed-up version of an integer-relation algorithm dating back more than 2,000 years to the Greek geometer Euclid of Alexandria (365–300 B.C.). The Euclidean ...

In this paper, a new mathematical method is used to study the indefinite equations of binary quadratic and binary arbitrary order, the problem of judging and solving these indefinite equations with or ...

Abstract: In this article, we present an efficient unified algorithm for the minimum Euclidean distance between two collections of compact convex sets, each of which can be a collection of convex ...