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integers

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Uchiha Sasuke
14/06/2019 at 02:06
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Find all positive integer values of n such that \(\dfrac{n-17}{n+23}\) is a square of a quotient number.

integers
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    Lux Arcadia 14/06/2019 at 14:20

    \(\dfrac{n-17}{n+23}=\dfrac{n+23-40}{n+23}=1-\dfrac{40}{n+23}\)

    \(\Rightarrow\left\{{}\begin{matrix}40⋮\left(n+23\right)\\n+23\ge23\left(n\ge0\right)\end{matrix}\right.\)

    \(\Leftrightarrow\left\{{}\begin{matrix}\left(n+23\right)\in\left\{1;2;4;5;8;10;20;40\right\}\\n+23\ge23\end{matrix}\right.\)

    \(\Leftrightarrow n+23=40\Leftrightarrow n=17\)


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Mr. Bee moderators
25/09/2018 at 09:30
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Find all integers $N$ such that $N^2-71$ is divisible by $7N+55$.

divisibilityintegers

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