Question

cmr:

\(\left(2015^{2017}+2017^{2015}\right)⋮2016\)

Answer 1

Lời giải:

Ta có:

\(A=2015^{2017}+2017^{2015}=2015^{2017}+1+2017^{2015}-1\)

Theo khai triển hằng đẳng thức:

\(2015^{2017}+1=2015^{2017}+1^{2017}=(2015+1)(2015^{2016}-2015^{2015}+....-2015+1)\vdots (2015+1)\)

\(\Leftrightarrow 2015^{2017}+1\vdots 2016\) (1)

Và: \(2017^{2015}-1=2017^{2015}-1^{2015}=(2017-1)(2017^{2014}+2017^{2013}+...+2017+1)\vdots (2017-1)\)

\(\Leftrightarrow 2017^{2015}-1\vdots 2016\) (2)

Từ (1),(2) suy ra \(A=2015^{2017}+2017^{2015}\vdots 2016\) (đpcm)

Answer 2

Nếu đúng tick em nha

2015^2017+2017^2015

=2015^2017+2017^2015-1

=(2015^2017+1^2017)+(2017^2015-1^2015)

Do 2015^2017+1^2017\(⋮\)2015+2=2016

2017^2015-1^2015\(⋮\)2017-1=2016

Vậy (2015^2017+2017^2015)\(⋮\)2016

Tick nha !