Question

Remainder when $(2{)}^{1004}$ is divided by 17 is

• A. 14
• B. 16
• C. 7
• D. 10

Answer 1

The correct option is B 16

$(2^4{)}^{250}$ x $2^4$
$(2^4{)}^{250}$ x $2^4$
$(17-1{)}^{250}$ x $2^4$
$=[250C0{17}^{250}-250C1{17}^{249}+250C2{17}^{248}-......-250C249{17}^1+{(-1)}^{250}]\times 2^4=(17m+1)\times 16$
Remainder, when the above term is divided by 17 is 16