Question

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

Answer 1

Answer: 9

$5^{99}=5^4.5^{95}$
$=625{\left[5^5\right]}^{19}$
$=625[3125{]}^{19}$
$=625[3124+1{]}^{19}$
$=625[11k\times 19+1]$
$=625\times 11k\times 19+625$
$=11k_1+616+9$
$=11\left(k_2\right)+9$
Remainder $=9$