Question

Chứng minh rằng 2018 mũ 2009 +1 chia hết cho 2019

Answer 1

`2018 equiv -1 (mod 2019)`

`=> (2018)^2009 equiv -1^2009 (mod 2019) equiv -1 (mod 2019)`

`=> 2018^2009 + 1 equiv -1 + 1 equiv 0 (mod 2019)`

Answer 2

Ta có: \(2018^{2009}+1\)

\(=\left(2018+1\right)\left(2018^{2008}-2018^{2007}+2018^{2006}-...+2018^2-2018+1\right)\)

\(=2019\left(2018^{2008}-2018^{2007}+2018^{2006}-...+2018^2-2018+1\right)\) ⋮2019