Diophantine Equations
With a Diophantine Equation we are only interested in integer solutions.
Puzzles
A Diophantine Equation is basically a puzzle: can you find integer solutions to a certain equation.
Pythagoras Theorem
Let's start with the famous Pythagoras' Theorem that we use for triangles:
Can you find integer solutions to it?
3, 4, 5
A well know integer solution is 3, 4, 5
Can you find other integer solutions? The page Pythagorean Triples talks all about them. But try to find some yourself first!
Powers of 3
How about the Pythagoras' Theorem but with powers of 3?
Can you find integer solutions?
Many have tried!