2025 AMC 8 Problems/Problem 11

Find the smallest positive integer $k$ such that $(2^{91}+k)$ is divisible by $127$ .

$\textbf{(A)}\ 122 \qquad \textbf{(B)}\ 123 \qquad \textbf{(C)}\ 124 \qquad \textbf{(D)}\ 125 \qquad \textbf{(E)}\ 126$

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