[tex]\displaystyle\bf\\a^2-12=n!,~a,n\in\mathbb{N}.\\a^2-12=n! \Leftrightarrow a^2=n!+12.\\o~solutie~simpla~pleaca~de~la~analizarea~ultimei~cifre.\\daca~n\geq 5~atunci~U(n!)=0.\\dar,~daca~s-ar~intampla~ca~n\geq 5~atunci~U(n!+12)=2,~iar~un~patrat~perfect~\\nu~poate~avea~ultima~cifra~2,~deci~n\in\left\{ 0,1,2,3,4 \right\}.\\analizand~aceste~patru~cazuri~vom~observa~ca~doar~n=4~este~solutie.\\daca~n=4,~atunci~a=6.\\[/tex]
