Question

demonstrati ca 3 la puterea la 80 - 2 la puterea 20 se divide cu 5 , repedeeeee

Answer 1

$5 | (3^{80}-2^{20}) ?$

$U(3^{1})=3$
$U(3^{2})=9$ }=>$U(3^{x}) \in${3;9;7;1}
$U(3^{3})=7$
$U(3^{4})=1$
............................................................
$U(3^{80})=U(3^{4*20})=U(3^{4})=1$


$U(2^{1})=2$
$U(2^{2})=4$ =>$U(2^{x})\in${2;4;8;6}
$U(2^{3})=8$
$U(2^{4})=6$
....................................................
$U(2^{20})=U(2^{4*5})=U(2^{4})=6$

=>$U(3^{80}-2^{20})=U(11-6)=U(5)=5$

=> $3^{80}-2^{20}$ se divide cu 5.

Am scris 11-6 in loc de 1-6 pt. ca (,) ca sa putem scadea am imprumutat 1 de la zeci.