How to find the remainder of (1099^5000)/99 ?

Principle: whole number x whole number is a whole number
Fraction times a whole number is fraction.
(1099)^5000/99
=(1099)/99*(1099)^4999
=(11 + 10/99)*1099^4999
=(11*1099^4999 +10*(1099/99)*(1099^4998)
The left term is a whole number.
Repeat the process 5000 times and we shall get:
=whole number +(10^5000)/99

The fractional part will give the remainder.
(10^5000)/99
=(100)^2500)/99
=(100/99)*(100^2499)
=(1 + 1/99)*(100^2499)
=1(100^2499)+ (1)(100/99)(100^2498)
The left term is a whole number.
Repeat the process 2500 times and we shall get:
=whole number +(1^2500)/99
= whole number+ 1/99

Thus, the remainder is 1