XYZ Tree

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

xyz-tree1

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 here? Warning: This is an unsolved problem in mathematics.

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.

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