24 Find all positive integers $x, y, z$, such that $3^{x}+4^{y}=5^{z}$.
24. Taking both sides of the equation modulo 3, we can see that $z$ is even, so $3^{x}+2^{2 y}$ is a perfect square. Thus, using the conclusion from Example 11 in Section 3.2, we can determine that $x=y=z=2$.