Question

Find the remainder when 1 raised to the power 2019 plus 2 raise to the power 2019 + 3 raise to the power 2019 plus.......... 2020 raised to the power 2019 is divided by 2019

Answer 1

there is a property that  (a to the power n)+(b to the power n) is always divisible by a+b if n is odd 

now in 
1^2019+2^2019.....2018^2019+2019^2019

(1^2019+2018^2019 )+(2^2019+2017^2019)+(3^2019+2016^2019) and so on...are divisible by 2019 according to the property 


now left number is 2019^2019 and we all know that it is divisible by 2019 so the remainder is 0.