Find the remainder when the $41$-digit number $1234\ldots$ is divided by $8$.
Find the remainder when \[6^{\underbrace{66\cdots6}_{100 \text{ times}}}\] is divided by 10.
If $(67^{67}+67)$ is divided by $68$, the remainder is:
What is the remainder when $1!+2!+3!+\cdots+100!$ is divided by $7$?
There are two integers 34041 and 32506, when divided by a three-digit integer $n$, leave the same remainder. What is the value of $n$?