[tex]\text{notatie: } \\
U(x) = \text{Ultima cifra a lui x.} \\ \\
\texttt{Vom folosi formula: }
U(\overline{ab}^n) = U(\overline{b}^n)\\ \\
Rezolvare: \\ \\
U(29^{2013}) = \\ \\ = U(9^{2013})= \\ \\ =U(9^{2012+1})= \\ \\
=U(9^{2012}\times 9) =\\ \\
=U(9^{2\times 1006}\times 9) =\\ \\
=U[(9^{2})^{1006}\times 9] =\\ \\
=U[81^{1006}\times 9] =\\ \\
=U[U(81^{1006}) \times 9] =\\ \\
=U[U(1^{1006}) \times 9] =\\ \\
= U[1\times 9] = \boxed{9}[/tex]
