5^100 is divided by 18. Then what is the remainder?  Choose the most appropriate option.
A) 10	B) 11	C) 13	D) 15	E) 16
Here N = 18=2×32   ϕ(18)=18(1−12)(1−13) = 6   So 56 when divided by 18, remainder is 1.   So we can write the given expression 5100=(56)16×54 = (1)16×54 = 52×52=7×7=49   Now 49 when divided by 18, remainder is 13.   13
<result>C</result>
5^100 is divided by 18. Then what is the remainder?