Question

Chứng minh 2016²⁰¹⁵ + 2018²⁰¹⁶ \(\\ ⋮\)2017

Answer 1

\(2016^{2015}\equiv2016\left(mod2017\right)\)

\(2018^{2016}\equiv1\left(mod2017\right)\)

Suy ra : \(2016^{2015}+2018^{2016}\equiv1+2016\equiv0\left(mod2017\right)\)

Vậy \(2016^{2015}+2018^{2016}⋮2017\)

Answer 2

\(2016\equiv-1\left(mod2017\right)=>2016^{2015}\equiv-1\left(mod2017\right)\)

\(2018\equiv1\left(mol2017\right)=>2018^{2016}\equiv1\left(mod2017\right)\)

\(=>2016^{2015}+2018^{2016}\equiv0\left(mod2017\right)\)