Question

VA ROG AJUTATI-MA!
a) ( $2^{n+} ^{1}$ - $2^{n}$ ) divizibil $2^{n}$ (nush cum sa pun 3 puncte asa ca am scris divizibil)
b) ( $3^{n+1}$ + $3^{n}$ ) divizibil 4
c) 21 | ( $5^{n+2}$ - $5^{n+1}$ + $5^{n}$ )
d) $2^{6n}$ | ( $8^{2n+1}$ + $4^{3n+1}$ - 11* $64^{n}$ )
AJUTOR VA ROGG!

Answer 1

^=la puterea
2^(n+1)-2^n=2^n(2^1-2^0)=2^n  divizibil cu 2^n

3^(n+1)+3^n=3^n(3^1 +3^0)=3^n * (3+1)=3^n * 4  deci divizibil cu 4

5^(n+2)-5^(n+1)+5^n=5^n(5^2-5^1+5^0)=5^n(25-5+1)=5^n * 21  deci divizibil cu 21

8^(3n+1)+4^(3n+1)-11*64^n=2^3*(3n+1)+2^2*(3n+1)-11*2^6n=

=2^(9n+3)+2^(6n+2)-11*2^6n=2^6n * [2^(3n+3)+2^2-11]  divizibil cu 2^6n