n is a positive integer, what is the remainder when 67

n is a positive integer, what is the remainder when 67^(2n+1) is divided by 8?

A) 1
B) 2
C) 3
D) 5
E) 7







67^(2k+1) will have the same remainder when divided by 8 as does 3^(2k+1), since 67 is 3 more than a multiple of 8.

3^(2k+1) =3 x 9^k =3 x (8+1)^k

As 9^k when divided by 8 yields a rem. of 1, 3 x 9^k will yield a rem. of 3