So for n being an integer what are the possible remainders for:

Start by looking at n = 1:

so the remainder is 1.

n= 2: so the remainder is 4. (No simplifying the fraction!)

n= 3: so the remainder is 2.

n= 4: so the remainder is 0.

n= 5: so the remainder is 7.

Continue by doing the long division:

Does this help?

-Dan