The 2 million dollars problem

The 2 million dollars math problem Do you think that someone would pay US dollars for the solution of a math problem? Yes, it happened in the history of mathematics that an award of this amount was offered for the solution of the following, apparently simple problem. Prove that there are no positive integers with […]

The Magic Sword: Modular Arithmetic

The Magic Sword: Modular Arithmetic It is common mathematical knowledge, and as we have seen in our previous posts,  equations are fundamental in mathematics. Solving equations is an important job and a lot of elementary problems are related to this field. Nevertheless, it turns out that in some cases we are interested not in exact […]

How to solve diophantine equations?

How to solve diophantine equations? I want to show you a method how to solve linear diophantine equations. The method works for equations in any number of variables. What if the “any number” is ? Well, if a linear equation of the form is given with the integers , then if is zero, then is […]

Diophantine equations

Diophantine equations Maybe the most familiar and important mathematical concept you meet in your math studies is equation. Mathematicians try to express the world in equations. Of course, there is no “World Equation”, but there are very famous equations which may have changed the world. Maybe Einstein’s E=mc2 from physics should come into your mind. […]