E=1+7^1+7^2+7^3+7^4+7^5+......+7^1995 divizibil cu 400
nr de termeni =1+1995=1996 putem sa ii grupam cate 4
E=(1+7^1+7^2+7^3)+7^4(1+7^1+7^2+7^3)+......7^1992(1+7^1+7^2+7^3)=
=(1+7+49+343)+7^4(1+7+49+343)+......7^1992(1+7+49+343)=
=400+7^4·400+......7^1992·400=
=400(1+7^4+...+7^1992) deci divizibil cu 400
F=13^1+13^2+13^3+13^4+13^5+13^6+....+13^2012 divizibil cu 7
nr de termeni =2012 putem sa ii grupam cate 2
F=13(1+13)+13^3(1+13)+13^5(1+13)+....+13^2011(1+13)=
=13·14+13^3·14+13^5·14+....+13^2011·14=
=14·(13+13^3+13^5+....+13^2011)=
=2·7·(13+13^3+13^5+....+13^2011) deci divizibil cu 7
G=1+5^+5^2+5^3+5^4+5^5+......+5^2012 divizibil cu 31
nr de termeni =1+2012=2013 se pot grupa cate 3
G=(1+5^1+5^2)+5^3(1+5^1+5^2)+......5^2010(1+5^1+5^2)=
=31+5^3·31+......5^2010·31=
=31·(1+5^3+......5^2010) deci divizibil cu 31
