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

or:How to find the remainder of (1099^5000)/99 ?or:Principle: whole number x whole number is a whole numberFraction times a whole number is frac

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

or:Principle: whole number x whole number is a whole numberFraction 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)/99The 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+ 1/99Thus, the remainder is 1

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