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2024 AMC 10A Problems/Problem 11

Revision as of 16:15, 8 November 2024 by MRENTHUSIASM (talk | contribs)

Problem

How many ordered pairs of integers $(m, n)$ satisfy $\sqrt{n^2 - 49} = m$?

$\textbf{(A)}~1\qquad\textbf{(B)}~2\qquad\textbf{(C)}~3\qquad\textbf{(D)}~4\qquad\textbf{(E)}$ Infinitely many

Solution

Note that $m$ is a nonnegative integer.

We square both sides, rearrange, and apply the difference of squares formula: \[(n+m)(n-m)=49.\]

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