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)
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 !
