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  4. The remainder obtained when 5124 is divided by 124 is

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Q. The remainder obtained when $5^{124 }$ is divided by $124$ is

KCETKCET 2007Binomial Theorem

Solution:

We have, $5^{124} = (5^3)^{41} . 5$
Now, $5^3 = 1 ( \text{mod} \; 124)$
$(5^3)^{41} = 1 ( \text{mod} \; 124)$
$(5^3)^{41} . 5 = 1.5 ( \text{mod} \; 124)$
$\Rightarrow \; 5^{124} = 5 ( \text{mod} \; 124)$