#Dqnghiep
C =4 + $4^{2}$+ $4^{3}$+ $4^{4}$+ ....+$4^{2014}$+ $4^{2015}$+ $4^{2016}$
=( 4 + $4^{2}$+ $4^{3}$)+($4^{4}$+$4^{5}$+$4^{6}$ )$+ ....+($4^{2014}$+ $4^{2015}$+ $4^{2016}$ )
=4 .( 1 + 4 + $4^{2}$) + $4^{4}$.( 1 + 4 + $4^{2}$) + ..... + $4^{2014}$.( 1 + 4 + $4^{2}$)
=4 . 21 + $4^{4}$. 21 +.....+ $4^{2014}$. 21
=21.(4 + $4^{4}$ +......+ $4^{2014}$) chia hết cho 21
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C =4 + $4^{2}$+ $4^{3}$+ $4^{4}$+ ....+$4^{2014}$+ $4^{2015}$+ $4^{2016}$
=( 4 + $4^{2}$)+ ($4^{3}$+$4^{4}$)+ ....+( $4^{2015}$+ $4^{2016}$ )
=4 .( 1 + 4 ) + $4^{3}$.( 1 + 4 ) + ..... + $4^{2015}$.( 1 + 4 )
=4 . 5 + $4^{4}$. 5 +.....+ $4^{2014}$. 5
=5.(4 + $4^{3}$ +......+ $4^{2015}$) chia hết cho 5
Vì C=4 + $4^{2}$+ $4^{3}$+ $4^{4}$+ ....+$4^{2014}$+ $4^{2015}$+ $4^{2016}$ chia hết cho 21;5 nên C chia hết cho 105
