What is the remainder when $2^{222} +22$ is divided by $2^{111}-2^{56}+1$?
$\textbf{(A) } 20 \qquad\textbf{(B) } 21 \qquad\textbf{(C) } 22 \qquad\textbf{(D) } 23 \qquad\textbf{(E) } 222$
Answer: B, 21, $x=2^{111}-2^{56}+1$ then $2^{222}=(x+2^{56}-1)^2\equiv (2^{112}-2\cdot 2^{56}+1)=2x-1$, so add 22 get 21, B
AMC 10/12 exam time:
A: Nov. 10, 2022
B: Nov 16, 2022
AMC 8: January, 17-23, 2023
Archive