Episode 10: Diophantine Equations

A Diophantine equation* is an equation in which only integer solutions are allowed.

For the following Diophantine equations, try and find all solutions (or show that there is no solution).

1. 2x²-5y²=5z²-1

2. (x²-21)(x²+2)=y⁹

3. a²+b²=11c²

*My Number Theory final is just going to entail solving 7 of these types of problems!