chứng minh C=5^1+5^2+5^3+5^4+…+5^2010 chia hết cho 6 và 31 chứng minh D=7^1+7^2+7^3+7^4+…+7^2010 chia hết cho 8 và 57

$C=5+5^2+…+5^{2010}$

$⇒C=5(1+5)+…+5^{2009}(1+2)$

$⇒C=5.6+…+5^{2009}.6$

$⇒C=6.(5+…+5^{2009})\vdots 6$

$C=5+5^2+5^3+…+5^{2010}$

$⇒C=5(1+5+5^2)+…+5^{2008}.(1+5+5^2)$

$⇒C=5.31+…+2^{2008}.31$

$⇒C=31.(5+…+5^{2008})\vdots 31$

$D=7+7^2+…+7^{2010}$

$⇒C=7(1+7)+…+7^{2009}(1+7)$

$⇒C=7.8+…+7^{2009}.8$

$⇒C=8.(7+…+7^{2009})\vdots 8$

$C=7+7^2+7^3+…+7^{2010}$

$⇒C=7(1+7+7^2)+…+7^{2008}(1+7+7^2)$

$⇒C=7.57+…+7^{2008}.57$

$⇒C=57.(7+…+7^{2008})\vdots 57$