There’s a rather beautiful algorithm for finding the greatest common divisor of two positive integers. For example, the greatest common divisor of 120 and 105 is 15. It’s clear that 15 is a divisor of ...

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 ...

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ABSTRACT: Numerous cryptographic algorithms (ElGamal, Rabin, RSA, NTRU etc) require multiple computations of modulo multiplicative inverses. This paper describes and validates a new algorithm, called ...

Computing the Euclidean minimum spanning tree (Emst) is a computationally demanding step of many algorithms. While work-efficient serial and multithreaded algorithms for computing Emst are known, ...

ABSTRACT: Let x and y be two positive real numbers with x y. Consider a traveler, on the interval [0, y/2], departing from 0 and taking steps of length equal to x. Every time a step reaches an ...

Finds the GCD using the euclidean algorithm or finds a linear combination of the GCD using the extended euclidean algorithm with all steps/work done shown ...