Question

Find the remainder when ${13}^{73}+{18}^5$ is divided by 11.

• A. 8
• B. 7
• C. 10
• D. 4

Answer 1

The correct option is B

7

$\frac{{13}^{73}}{11}\mid r=\frac{2^{73}}{11}\mid r=\frac{{32}^{14}\times 8}{11}\mid r=(-1{)}^{14}\times 8=8$
Similarly , $\frac{{18}^5}{11}\mid r=\frac{7^5}{11}\mid r=\frac{343\times 49}{11}\mid r=2\times 5=10$
So, the remainder $=8+10=\frac{18}{11}\mid r=7$.