If x = 1^99 + 2^99 + 3^99 + 4^99 + 5^99, then find the number which divides x.

This can be solved by remainder theorem,that is by finding out the unit digit of every num.1^99 will always end with 1.5^99 will always end with 5Now 2^99 can be written as (2^4)^24 × 2^3 as we know 2^4 will always end with 6 hence (2^4)^24 will also end with 6 and × (2^3=8) the last digit will be 8.Similarly 3^99 can be written (3^4)^24 × 3^3 which will end with 7.And 4^99 can be written as (4^2)^49 × 4 which will end with 4.Hence adding all unit digits 1+8+7+4+5=25 Last digit is 5 means the num is divisible by 5 - ans