877*. Does the equation

$$
x^{2}+y^{3}+z^{4}=10^{25}
$$

have a solution in natural numbers?
$\triangle$ Let's use the equality

$$
1^{2}+2^{3}+1^{4}=10
$$

Multiply it by $10^{24}$. Why exactly by $10^{24}$? Firstly, because $10 \cdot 10^{24}=10^{25}$, and secondly, because 24 is divisible by 2, 3, and 4. By comparing the resulting numerical equality

$$
10^{24}+2^{3} \cdot 10^{24}+10^{24}=10^{25}
$$

with the given equation, we find one of the solutions to the equation in natural numbers.

Answer: it has, for example, $x=10^{12}, y=2 \cdot 10^{8}, z=10^{6}$.