2025 AMC 12A Problems/Problem 1

The following problem is from both the 2025 AMC 10A #1 and 2025 AMC 12A #1, so both problems redirect to this page.

Problem

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

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

2025 AMC 10A (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

2025 AMC 12A (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions