Question

cmr 2005^2007+2007^2005 chia hét cho 2006

 

Answer 1

\(2005^{2007}+2007^{2005}\)

\(=\left(2005^{2017}+1^{2017}\right)+\left(2007^{2005}-1^{2005}\right)\)

Vì \(2005^{2007}+1^{2007}⋮2005+1=2006;2007^{2005}-1^{2005}⋮2007-1=2006\)

\(\Rightarrow\)\(\left(2005^{2007}+1^{2007}\right)+\left(2007^{2005}-1^{2005}\right)⋮2016\)

\(\Rightarrow\)\(2005^{2007}+2007^{2005}⋮2006\)( đpcm )