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The remainder obtained when $5^{124}$ is divided by 124 is
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Verified Answer
The correct answer is:
5
We have, $5^{124}=\left(5^{3}\right)^{41} \cdot 5$
Now, $\quad 5^{3}=1(\bmod 124)$
$\therefore \quad\left(5^{3}\right)^{41}=1(\bmod 124)$
$\left(5^{3}\right)^{41} \cdot 5=1 \cdot 5(\bmod 124)$
$\Rightarrow \quad 5^{124}=5(\bmod 124)$
Now, $\quad 5^{3}=1(\bmod 124)$
$\therefore \quad\left(5^{3}\right)^{41}=1(\bmod 124)$
$\left(5^{3}\right)^{41} \cdot 5=1 \cdot 5(\bmod 124)$
$\Rightarrow \quad 5^{124}=5(\bmod 124)$
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