`a) M = 7^0+ 7^1+ 7^2+7^3+...+7^2018+7^2019`
`= (7^0+ 7^1)+ (7^2+7^3)+...+(7^2018+7^2019)`
`= 7^0 . 8 + 7^2 . 8 + ....+ 7^2018 . 8`
`= 8 . (7^0 + 7^2 + ...+7^2018)`
mà `8 vdots 8`
`=> 8 . (7^0 + 7^2 + ...+7^2018) vdots 8`
`=> M vdots 8` (đpcm)
b) Ta có: `180 vdots 90; 270 vdots 90; 90 vdots 90`
`=> UCLN(a;b;c) = 90`
Lại có:
`B(a) = {0;90;180;270;360;450;540;630;..}`
`B(b) = {0;180;360;540;720`
`B(c) = {0;270;540;810;...}`
`=> BCN``N(a;b;c) = 540`
(Chúc bạn học tốt)