**Category:** 3D Objects & 2D Shapes, Variables & Equations, and Relations & Functions**Suitable for Grade Level:** Elementary and Secondary

**The Math in this Problem:**

This math puzzle introduces us to the Markov Diophantine equation, in which a Markov number is a positive integer x, y, or z that is part of its solution. Experimenting with various numbers, students are challenged to come up with a few of the many triple solutions to this formula, which was named after Russian Mathematician Andrey Markov.

Find 3 positive integers x, y and z which satisfy this equation:

Using this solution, find a different solution by changing one and only one of the numbers.

How many solutions does the equation have?

## Hint

#### Extensions:

- Are all triple solutions {X,Y,Z} which contain a number, N, connected to each other on the tree found in the hint above?
**Warning**: This is an unsolved problem in mathematics.