Question

câu 1: c/m :\(5^{2014} -5^{2013} +5^{2012}\) chia het cho 105

Answer 1

Ta có: \(5^{2014}-5^{2013}+5^{2012}=5^{2011}\left(5^3-5^2+5\right)\)

\(=5^{2011}.105⋮105\)

\(\Rightarrow5^{2014}-5^{2013}+5^{2012}⋮105\left(đpcm\right)\)

Vậy...

Answer 2

ta có:

\(5^{2014}-5^{2013}+5^{2012}\)

\(=5^{2012}\left(5^2-5+1\right)\)

\(=5^{2012}\left(25-5+1\right)\)

\(=5^{2012}.21\)

ta thấy: \(5^{2012}.21⋮21\)

\(5^{2012}.21⋮5\)

\(\Rightarrow5^{2012}.21⋮21.5\)

\(\Rightarrow5^{2012}.21⋮105\)

\(\Leftrightarrow5^{2014}-5^{2013}+5^{2012}⋮105\left(đpcm\right)\)