Thomas Jefferson’s first draft of the Declaration of Independence read: “We hold these truths to be sacred and undeniable . . . ” It was supposedly Benjamin Franklin who suggested instead announcing ...

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 ...

Explore the intersection of AI, game theory, and behavioral strategies. Explore the intersection of AI, game theory, and behavioral strategies. Explore the intersection of AI, game theory, and ...

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.

The Greatest Common Factor (GCF) is the largest integer that divides two or more numbers without leaving a reminder. GCF plays a significant role in various mathematical calculations, such as ...

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 ...

Abstract: A new parallelization of the extended Euclidean GCD algorithm is proposed. It matches the best existing integer GCD algorithms since it can be achieved in parallel O/sub eps/(n/log n) using ...