hogann wrote:

If x is a positive integer, what is the remainder when 7^(12x+3) + 3 is divided by 5?

A. 0

B. 1

C. 2

D. 3

E. 4

Binomial method works well here.

First lets assume x=1

so 7^12x+3 + 3 / 5 what is the remainder?

7^15 + 3 /5

(5+2)^15 / 5, all terms will be divisible by 5 except 2^15

What is remainder of 2^15 / 5?

2^15 = 2* 4^7 = 2(5-1)^7

All terms will again be divisible by 5 except -1^7

Then -1*2 = -2 + 3 = 1

Hence we have a remainder of 1 when divided by 7

Answer is thus B

Cheers!

J

Just wondering is it possible to multiply both numerator and denominator by 2 in order to get 10 as denominator? That way we would only need to worry about the units digit of the expression