Răspuns:
Explicație pas cu pas:
a) n=5+5²+5³+5⁴+....+5⁵⁰= (5+5³)+(5²+5⁴)+(5⁵+5⁷)+....+(5⁴⁷+5⁴⁹)+(5⁴⁸+5⁵⁰)=
5(1+25)+5²(1+25)+5⁵(1+25)+...+5⁴⁷(1+25)+5⁴⁸(1+25)= 26(5+5²+5⁵+....5⁴⁸) divizibil cu 26
b) n=2+2²+2³+2⁴+....+2⁵¹=(2+2²+2³)+(2⁴+2⁵+2⁶)+(2⁷+2⁸+2⁹)+....+(2⁴⁹+2⁵⁰+2⁵¹)=
2(1+2+4)+2⁴(1+2+4)+2⁷(1+2+4)+....+2⁴⁹(1+2+4)= 7(2+2⁴+2⁷+...+2⁴⁹) divizibil cu 7
