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If $(24,92)=24 m+92 n$, then $(m, n)$ is
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Verified Answer
The correct answer is:
$(4,-1)$
Since, $\quad 92=3 \cdot 24+20$
$24=1 \cdot 20+4$
$20=4 \cdot 5+0$
$\therefore \quad(24,92)=4$
$=24-1 \cdot 20$
$=24-1 \cdot(92-3 \cdot 24)$
$=24-92+3 \cdot 24$
$=4 \cdot 24-92$
But $(24,92)=24 m+92 n$
$\therefore$ From Eqs. (i) and (ii), we get
$$
\begin{aligned}
\mathrm{m} &=4 \text { and } \mathrm{n}=-1 \\
\therefore \quad(\mathrm{m}, \mathrm{n}) &=(4,-1)
\end{aligned}
$$
$24=1 \cdot 20+4$
$20=4 \cdot 5+0$
$\therefore \quad(24,92)=4$
$=24-1 \cdot 20$
$=24-1 \cdot(92-3 \cdot 24)$
$=24-92+3 \cdot 24$
$=4 \cdot 24-92$
But $(24,92)=24 m+92 n$
$\therefore$ From Eqs. (i) and (ii), we get
$$
\begin{aligned}
\mathrm{m} &=4 \text { and } \mathrm{n}=-1 \\
\therefore \quad(\mathrm{m}, \mathrm{n}) &=(4,-1)
\end{aligned}
$$
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