[tex]\displaystyle\\Fie~a~si~b~doua~numere~intregi,~daca~a|b~si~b|a~\Longleftrightarrow a=\pm b,\\\underline{Demonstratie}~:\\Din~a|b \Longleftrightarrow \exists k_1\in\mathbb{Z}~a.i.~b=ak_1.~(1)\\Din~b|a \Longleftrightarrow \exists k_2\in\mathbb{Z}~a.i.~ a=bk_2.~(2)\\Inmultim~cele~doua~relatii,~obtinem~:~ab=abk_1k_2 \Longleftrightarrow k_1k_2=1,~cum\\k_1~si~k_2~sunt~numere~intregi~obtinem~k_1=k_2=\pm 1,~de~unde~a=\pm b.\\--------------------------------[/tex]
[tex]\displaystyle\\(n+7)|(2n-8),~(2n-8)|(n+7) \Longleftrightarrow n+7=\pm (2n-8).\\Daca~n+7=2n-8,~obtinem~n=15.\\Daca~n+7=8-2n,~obtinem~n=\frac{1}{3},~care~nu~este~numar~natural,\\deci~n=15.[/tex]
