Question

Arătați ca nr :
A=9la2002-7la2000eate diviziunile cu 10

Answer 1

$A=9^{2002}-7^{2000}$

$A=(3^{2})^{2002}-7^{2000}$

$A=3^{4004}-7^{2000}$



OBS!!!

$\boxed{\text{Un numar este divizibil cu 10 daca are ultima cifra 0!}}$



$U(A)=U(3^{4004}-7^{2000})$


$U(3^{4004})=?$

$U(3^{1})=3$

$U(3^{2})=9$

$U(3^{3})=7$

$U(3^{4})=1$

......................................................................

$U(3^{4004})=U(3^{1001*4})=U(3^{4})=1$



$U(7^{2000})=?$


$U(7^{1})=7$

$U(7^{2})=9$

$U(7^{3})=3$

$U(7^{4})=1$

......................................................................

$U(7^{2000})=U(7^{500*4})=U(7^{4})=1$



$U(A)=U(3^{4004}-7^{2000})=$

$=U(1-1)=$

$=U(0)=$

$\boxed{=0}$

$\boxed{\text{U(A)=0 rezulta A este divizibil cu 10}}$