## Question

**When (67**^{67} +67) is divided by 68, the remainder is** _____**

^{67}+67) is divided by 68, the remainder is

A. 0

B. 22

C. 33

D. 66

**Answer:** D

**Solution:**

(x^{n}+1) is divisible by (x+1) when n is odd.

=> (67^{67} + 1) is divisible by (67 + 1)

=> (67^{67} + 1) is divisible by 68

=> (67^{67}+1) ÷ 68 gives a remainder of 0

=> [(67^{67}+1) + 66] ÷ 68 gives a remainder of 66

=> (67^{67} + 67) ÷ 68 gives a remainder of 66