Question

Find the digit at the unit place in number 2019^2020+2020^2019

Answer 1

Answer: 1

Use the method of cyclicity.

Observe that the unit digit of 2019^2018 will be the same as 9^2018 as it won't be affected by others. So, we need to find the units digit of 9^2018

Observe the pattern  --

9^1=9

9^2=81(unit digit 1)

9^3=729(unit digit 9)

9^4=6561(unit digit 1)

So, in every odd power unit digit is 9 and every even power unit digit is 1. So, the unit digit of 2019^2020=1

Same way using cyclicity , 2020^2019 will be the same as 0^2019 and 0 to the power of any number gives 0

So we have to add 1 + 0 which gives 1 as answer.