Question

Verifica dacă sunt prime numerele:
a= 712•10 la puterea 5-1
b= 3 la puterea 40+2 la puterea 42
Urgggeent!!!!

Answer 1

 

$\displaystyle\bf\\a=712\times10^5-1\\\\a=712\times100000-1\\\\a=712\underbrace{00000}_{5~de~0}-1\\\\a=711\underbrace{99999}_{5~de~9}\\\\Adunam~cifrele.\\\\7+2\times1+5\times9=7+2+45=9+45=54\\\\54~\vdots~9\\\\\implies~~a~\vdots~9\\\\\implies~~a~NU~este~numar~prim.$

.

$\displaystyle\bf\\b=3^{40}+2^{42}\\\\Calculam~ultima~cifra~a~numarului~b.\\\\U(b)=U\Big(3^{40}\Big)+U\Big(2^{42}\Big)=\\\\=U\Big(3^{4\times10}\Big)+U\Big(2^{4\times10+2}\Big)=\\\\=U\left(\Big(3^4\Big)^{10}\right)+U\left(\Big(2^4\Big)^{10}\times2^2\Big)\right)=\\\\\\=U\Big(81^{10}\Big)+U\Big(16^{10}\times4\Big)=\\\\=U\Big(1^{10}\Big)+U\Big(6^{10}\times4\Big)=\\\\=U\Big(1}\Big)+U\Big(6\times4\Big)=\\\\=1+U\Big(24\Big)=\\\\=1+4=5\\\\\implies~b~\vdots~5\\\\\implies~b~NU~este~numar~prim.$