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What is the remainder when $2^{7^{8^{1}}}+ 5^{3^{3^{5}}}$ is divided by $10^{10}$?

How many decimal digits does $2781!$ have?

For example, $5! = 120$ has $3$ decimal digits.

$x^y-y^x=xy^2-19$

Solve the equation above for primes $x$ and $y$. Given that there are two solution pairs $(x_1, y_1)$ and $(x_2, y_2)$, find the value of ...

$\text{For some positive integers }\mathbf{A, B, C}\text{ and }\mathbf{D}\text{ the following equation is true.}$

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