Tetracija je ponovljeno potenciranje i označava se ovako:
gdje se
na desnoj strani pojavi točno
puta.
Nadalje, takve potencije se računaju odozgo prema dolje. Na primjer,
i
. Odredi:
Tetration is repeated exponentiation and it is denoted like so:
where
appears exactly
times on the right.
Furthermore, they are calculated from top to bottom. For example,
and
. Determine:
[lang=hr]
Tetracija je ponovljeno potenciranje i označava se ovako: $^{n}{a} = a^{a^{\dots^{a}}}$ gdje se $a$ na desnoj strani pojavi točno $n$ puta. \\
Nadalje, takve potencije se računaju odozgo prema dolje. Na primjer, $^{3}{3} = 3^{3^3} = 3^{\left( 3^3 \right) } = 3^{27} = 7625597484987$ \\
i $^{4}{2} = 2^{2^{2^2}} = 2^{\left( 2^{ \left( 2^2 \right) } \right) } = 2^{\left(2^4 \right) } = 2^{16} = 65536$. Odredi: \\~\\~
\begin{center}$ ^{1}{1} \;\cdot\; ^{2}{2} \;\cdot\; ^{3}{3} \;\cdot\; ^{4}{4} \;\cdot\; ... \;\cdot\; ^{111}{111} \pmod{11111111111111} $\end{center}
[/lang]
[lang=en]
Tetration is repeated exponentiation and it is denoted like so: $^{n}{a} = a^{a^{\dots^{a}}}$ where $a$ appears exactly $n$ times on the right. \\
Furthermore, they are calculated from top to bottom. For example, $^{3}{3} = 3^{3^3} = 3^{\left( 3^3 \right) } = 3^{27} = 7625597484987$ \\
and $^{4}{2} = 2^{2^{2^2}} = 2^{\left( 2^{ \left( 2^2 \right) } \right) } = 2^{\left(2^4 \right) } = 2^{16} = 65536$. Determine: \\~\\~
\begin{center}$ ^{1}{1} \;\cdot\; ^{2}{2} \;\cdot\; ^{3}{3} \;\cdot\; ^{4}{4} \;\cdot\; ... \;\cdot\; ^{111}{111} \pmod{11111111111111} $\end{center}
[/lang]
