The remainder when 5^ 99 is divided by 13 is - Vidyadip

MCQ

The remainder when ${5^{99}}$ is divided by $13$ is

A
$6$
✓
$8$
C
$9$
D
$10$

✓

Answer

Correct option: B.

$8$

b
(b) ${5^{99}} = (5)\,{({5^2})^{49}} = 5{(25)^{49}} = 5{(26 - 1)^{49}}$

= $5 \times (26) \times ({\rm{Positive terms)--5,}}$ So when it is divided by $13$ it gives the remainder $-5$ or $(13 -5)$ $i.e.,$ $8$.

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