Question

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

• A. 0
• B. 5
• C. 1
• D. 2

Answer 1

Answer: (B)

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