Question

Chứng minh rằng 7²⁰¹⁸ + 7²⁰¹⁷ - 7²⁰¹⁶ chia hết cho 11

Answer 1

\(7^{2018}+7^{2017}-7^{2016}\)

\(=7^{2016}\left(7^2+7-1\right)=7^{2016}.55⋮11\)

\(\Rightarrowđpcm\)

Answer 2

\(7^{2018}+7^{2017}-7^{2016}\)

\(=7^{2016}\left(7^2+7-1\right)\)

\(=7^{2016}.55⋮11\)

\(\Rightarrow\) đpcm

Answer 3

\(7^{2018}+7^{2017}-7^{2016}\)

\(=7^{2016}.7^2+7^{2016}.7-7^{2016}.1\)

\(=7^{2016}.49+7^{2016}.7-7^{2016}.1\)

\(=7^{2016}\left(49+7-1\right)\)

\(=7^{2016}.55\)

\(=7^{2016}.11.5⋮11\)

\(\Rightarrowđpcm\)

Answer 4

\(7^{2018}+7^{2017}-7^{2016}\)

\(=7^{2016}.7^2+7^{2016}.7-7^{2016}.1\)

\(=7^{2016}.49+7^{2016}.7-7^{2016}.1\)

\(=7^{2016}.\left(49+7-1\right)\)

\(=7^{2016}.55\)

\(=7^{2016}.11.5⋮11\left(đpcm\right)\)