Teorema lui Fermat
Daca p numar prim si n numar natural nenul astfel incat (n,p)=1 atunci
[tex](n^{p-1}-1)\vdots p\leftrightarrow(n^p-p)\vdots p\\
2^{70}=(2^5)^{13}\cdot 2^5=32^{13}\cdot 32\\
Din\ teorema\ (32^{13}-32)\vdots 13\rightarrow32^{13}=13m+32\\
2^{70}=32(13m+32)\\
3^{70}=(3^5)^{13}\cdot 3^5=243^{13}\cdot 243\\
Din\ teorema\ (243^{13}-243)\vdots 13\rightarrow 243^{13}=13k+243\\
3^{70}=243(13k+243)\\
2^{70}+3^{70}=32(13m+32)+243(13k+243)=\\
=13(32m+243k)+32^2+243^2=\\
=13(32m+243k)+13\cdot 4621=\\
=13(32m+243k+4621)\vdots13[/tex]
