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Difference between revisions of "2024 AMC 10A Problems/Problem 11"

m (Protected "2024 AMC 10A Problems/Problem 11" ([Edit=Allow only administrators] (expires 04:59, 8 November 2024 (UTC)) [Move=Allow only administrators] (expires 04:59, 8 November 2024 (UTC))) [cascading])
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== Problem ==
  
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How many ordered pairs of integers <math>(m, n)</math> satisfy <math>\sqrt{n^2 - 49} = m</math>?
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<math>\textbf{(A)}~1\qquad\textbf{(B)}~2\qquad\textbf{(C)}~3\qquad\textbf{(D)}~4\qquad\textbf{(E)}</math> Infinitely many
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== Solution ==
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Note that <math>m</math> is a nonnegative integer.

Revision as of 16:13, 8 November 2024

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.

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