[tex] 3^{a} +3^{b} +3^{c} =811. \\ ~\text{Daca}~a \neq0; b \neq0; c \neq 0\Rightarrow~Suma~{\vdots}~3. \\
\text{Dar}~3~$\nmid811\Rightarrow~a,b~sau~c~=0\Rightarrow~\text{U.C.~a~produsului~este~0.}\\
\text{Obs.:~Putem~afla~b~si~c.~Fie}~\underline{a=0}\Rightarrow1+3^{b} +3^{c} =811\Rightarrow 3^{b} +3^{c} =810. \\
\text{Se~observa~ca~729+81=810}\Rightarrow \underline{b=6}\Rightarrow\underline{c=4}. \\
\text{Deci,}~a\cdot b\cdot c=0\cdot 6\cdot 4=0.~\\\text{Produsul~este~\fbox{0}}\Rightarrow \text{ultima~cifra~este~0.}[/tex]
