Question

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

Answer 1

The correct answer is 9.
599=54.595
=625[55]19
=625[3125]19
=625[3124+1]19
=625[11k×19+1]
=625×11k×19+625
=11k1​+616+9
=11(k2​)+9
Remainder =9