Question

The remainder when
$x=5^{5^{{.}^{{.}^5}}}$ ($24$ times $5$)
is divided by $24$ is

• A. $1$
• B. $3$
• C. $5$
• D. $23$

Answer 1

The correct option is C $5$

Note that
$x=5^{5^{{.}^{{.}^5}}}$ ($23$ times $5$)
is an odd natural number. Therefore
$x=5^{2ni+1}=({25}^m{)}^5$
where $m$ is a natural number. Thus,
$x={(24+1)}^{m}5=5+$a multiple of $24$.
Hence, the desired remainder is $5$.