Table of Contents
What are Diophantine equations used for?
The purpose of any Diophantine equation is to solve for all the unknowns in the problem. When Diophantus was dealing with 2 or more unknowns, he would try to write all the unknowns in terms of only one of them.
What is the meaning of Diophantine equation?
In mathematics, a Diophantine equation is a polynomial equation, usually involving two or more unknowns, such that the only solutions of interest are the integer ones (an integer solution is such that all the unknowns take integer values).
Who discovered Diophantine equation?
Diophantus of Alexandria
The first known study of Diophantine equations was by its namesake Diophantus of Alexandria, a 3rd century mathematician who also introduced symbolisms into algebra. He was author of a series of books called Arithmetica, many of which are now lost.
What is the pronunciation of diophantus?
Break ‘diophantus’ down into sounds: [DY] + [OH] + [FAN] + [TUHS] – say it out loud and exaggerate the sounds until you can consistently produce them.
What is a Diophantine equation?
In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).
What is the difference between linear and exponential Diophantine?
A linear Diophantine equation equates the sum of two or more monomials, each of degree 1 in one of the variables, to a constant. An exponential Diophantine equation is one in which exponents on terms can be unknowns.
Can factoring crack a Diophantine equation wide open?
Sometimes factoring can crack a Diophantine equation wide open. Instead of talking about how good and powerful it is, let’s see a demonstration of how factoring can help solving certain Diophantine equations. We’re going to start off with quadratic equations, which we already know how to factorize.