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 ...

ABSTRACT: 1) Fermat has proved that x 4 + y 4 = z 2 has no positive integer solution, and in 2011, J. Cullen [1] reported that x,y∈{ 0,1,⋯, 10 7 } , x 4 + y 4 +1 is not a square greater than 1, and ...

This program offers a C++ solution to compute the Greatest Common Divisor (GCD) of two strings, showcasing an application of the Euclidean algorithm for string manipulation.

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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, ...

My solutions to Google's Foobar Challenge for coding data structures and algorithms. Includes my solution code, unit tests, background notes, design notes, and references.

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 ...