Divisibility problem with modular arithmatic Here's the question:
"When an integer $n$ is divided by 6, the remainder is 5. What are the possible values of the remainder when $9n$ is divided by 8?"
I'm not entirely sure how to decipher this questions because I'm having a hard time understanding it. Does the first part mean: $n = 6k + 5$ where $5$ being the remainder? 

The possible answers are 1,3,5 and 7.
Here's how to solve it.
First, note that since the remainder when divided by 6 is 5, we know that $n = 6k + 5$ 
So, $9n = 9(6k+5) \equiv (48k + 40) + (6k + 5) \equiv (6k + 5)\mod{8}$.
So, $9n \equiv (6k + 5)\mod{8}$.
Also note that 6m + 5 = 6(m+4) + 5 (mod 8), so the remainders repeat with a period of 4. So we only need to find the values for k = 0,1,2 and 3 (or any other four consecutive integers) to obtain all possible remainders. Which gives 1,3,5 and 7
