7.
multiplii lui 3 ___
6,33,39,45,48,111,xxx 3×107, 3×49+3×50, 3×n
8. 1+7+7²+7³+7⁴+7⁵+7⁶+7⁷+7⁸+7⁹+7¹⁰+7¹¹=
= (1+7+7²)+7³ *(1+7+7²)+7⁶ *(1+7+7²)+7⁹ *(1+7+7²)=
= (1+7+49) *(1+7³+7⁶+7⁹)=
= 57*(1+7³+7⁶+7⁹)=
= 3*19*(1+7³+7⁶+7⁹) deci divizibil cu 3
9. 1+2+2²+2³+2⁴+2⁵+2⁶+..+2⁹⁶+2⁹⁷+2⁹⁸+2⁹⁹=
nr termeni 99+1=100 se pot grupa cate 4
=( 1+2+2²+2³)+2⁴( 1+2+2²+2³)+..+2⁹⁶( 1+2+2²+2³)=
=( 1+2+4+8) *(1+2⁴+..+2⁹⁶)=
=15 *(1+2⁴+..+2⁹⁶) deci divizibil cu 15
