18. Find the remainder when $2^{55}+1$ is divided by 33 .
18: Answer: 0
Note that $x^{11}+1$ is divisible by $x+1$ by Factor Theorem. Hence $2^{55}+1=32^{11}+$ 1 is divisible by $32+1=33$, ie. $2^{55}+1$ is divisible by 33 .