The remainder on dividing 5^ 99 by 11 is - Vidyadip

MCQ

The remainder on dividing $5^{99}$ by $11$ is

✓
$9$
B
$18$
C
$27$
D
$36$

✓

Answer

Correct option: A.

$9$

a
$5^{99}=5^4 \cdot 5^{95}$

$=625\left[5^5\right]^{19}$

$=625[3125]^{19}$

$=625[3124+1]^{19}$

$=625[11 k \times 19+1]$

$=625 \times 11\,k \times 19+625$

$=11\,k _1+616+9$

$=11\left( k _2\right)+9$

Remainder $=9$

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