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2024 DMC Mock 10 Problems/Problem 13

Revision as of 12:13, 22 December 2024 by Pateywatey (talk | contribs) (Created page with "Let the integer we are trying to find be <math>x</math>. Then, <math>x</math> satisfies <math>\frac{48}{x^2}+x=7</math>. Since <math>x</math> and <math>7</math> are both inte...")
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Let the integer we are trying to find be $x$.

Then, $x$ satisfies $\frac{48}{x^2}+x=7$. Since $x$ and $7$ are both integers, $\frac{48}{x^2}$ must also be an integer. $x$ must be $\pm 1,2,4$. Guess and check yields $x=4$. $4$ has $\boxed{3}$ factors.

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