Folklore

Certainly or infinitely many natural solutions does the equation $x^{2}+y^{3}=z^{2}$ have?
One of the solutions to the equation is $(1,2,3)$. On the other hand, if ( $x, y, z$ ) is a solution, then ( $8 x, 4 y, 8 z$ ) is also a solution.

## Answer

Infinite.