Question

Find the value of (2019 20202020)
(2020 20192019) ?​

Answer 1

Answer:

2019 = -1 (mod 2020)

=> 2019 when raised to an even power gives 1 (mod 2020) and gives -1 (mod 2020) when raised to an odd power.

(

2019^2n = -1^2n (mod 2020) = 1(mod 2020).

2019^(2n+1) = -1^(2n) *-1 (mod 2020) = -1(mod2020)

)

=> 2019^2019 = -1 (mod 2020) = 2019 .

Therefore, 2019^2019 leaves a remainder of 2019 when divided by 2020.