Vrijeme: 23:18
Nepotrebno bezobrazni | Unnecessarily rude #4
Odredi:
Napomena: cik-cak potencije se isto računaju odozgo prema dolje. Na primjer, 
Determine:
Remark: zigzag powers are also calculated from top to bottom. For example,
[lang=hr]
Odredi:
\[
\scriptspace=0pt
\begingroup
\scriptspace=0pt
\setbox32=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$111$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$111$}%
\advance\dimen0-\wd0%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox32=\hbox{$\displaystyle {\displaystyle \vdots\;\;\;}^{\raise0.15em\hbox to 0pt{$\displaystyle \box32 $\hss}}
$}
\setbox32=\hbox{$\displaystyle {}^{\raise0.15em\hbox to 0pt{\hss$\displaystyle \box32 $}}{\displaystyle \;\;\;\vdots}
$}
\setbox32=\hbox{$\displaystyle {\displaystyle 111}^{\raise0.15em\hbox to 0pt{$\displaystyle \box32 $\hss}}
$}
\setbox32=\hbox{$\displaystyle {}^{\raise0.15em\hbox to 0pt{\hss$\displaystyle \box32 $}}{\displaystyle 111}
$}
\setbox32=\hbox{$\displaystyle {\displaystyle 111}^{\raise0.15em\hbox to 0pt{$\displaystyle \box32 $\hss}}
$}
\setbox33=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$5$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$5$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$5$}%
\advance\dimen0-\wd0%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$5$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$5$}%
\advance\dimen0-\wd0%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox34=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$4$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$4$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$4$}%
\advance\dimen0-\wd0%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$4$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox35=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$3$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0-\wd0%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox36=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$2$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$2$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
1 \;\cdot\;\; \box36 \;\;\cdot \;\; \box35 \;\;\cdot\;\; \box34 \;\;\cdot\;\; \box33 \;\;\cdot \;\; \dots \;\; \cdot \;\; \box32 \;\;\;\;\;\;\pmod{11111111111111}
\endgroup
\]\\~\\~\\~
Napomena: cik-cak potencije se isto računaju odozgo prema dolje. Na primjer,
\[
\scriptspace=0pt
\begingroup
\scriptspace=0pt
\setbox32=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$3$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$7625597484987$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox33=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$3$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$27$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox34=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$3$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox35=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$3$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0-\wd0%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\box35 \;\;=\;\; \box34 \;\;=\;\; \box33 \;\;=\;\; \box32
\endgroup
\]
[/lang]
[lang=en]
Determine:
\[
\scriptspace=0pt
\begingroup
\scriptspace=0pt
\setbox32=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$111$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$111$}%
\advance\dimen0-\wd0%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox32=\hbox{$\displaystyle {\displaystyle \vdots\;\;\;}^{\raise0.15em\hbox to 0pt{$\displaystyle \box32 $\hss}}
$}
\setbox32=\hbox{$\displaystyle {}^{\raise0.15em\hbox to 0pt{\hss$\displaystyle \box32 $}}{\displaystyle \;\;\;\vdots}
$}
\setbox32=\hbox{$\displaystyle {\displaystyle 111}^{\raise0.15em\hbox to 0pt{$\displaystyle \box32 $\hss}}
$}
\setbox32=\hbox{$\displaystyle {}^{\raise0.15em\hbox to 0pt{\hss$\displaystyle \box32 $}}{\displaystyle 111}
$}
\setbox32=\hbox{$\displaystyle {\displaystyle 111}^{\raise0.15em\hbox to 0pt{$\displaystyle \box32 $\hss}}
$}
\setbox33=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$5$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$5$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$5$}%
\advance\dimen0-\wd0%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$5$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$5$}%
\advance\dimen0-\wd0%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox34=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$4$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$4$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$4$}%
\advance\dimen0-\wd0%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$4$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox35=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$3$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0-\wd0%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox36=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$2$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$2$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
1 \;\cdot\;\; \box36 \;\;\cdot \;\; \box35 \;\;\cdot\;\; \box34 \;\;\cdot\;\; \box33 \;\;\cdot \;\; \dots \;\; \cdot \;\; \box32 \;\;\;\;\;\;\pmod{11111111111111}
\endgroup
\]\\~\\~\\~
Remark: zigzag powers are also calculated from top to bottom. For example,
\[
\scriptspace=0pt
\begingroup
\scriptspace=0pt
\setbox32=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$3$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$7625597484987$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox33=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$3$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$27$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox34=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$3$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\setbox35=\hbox{$\displaystyle \hbox{%
\dimen0=0pt\dimen2=0pt%
\dimen8=\fontdimen13\textfont2\advance\dimen8 0.15em%
\setbox0=\hbox{$3$}%
\dimen6=\wd0%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0\dimen4%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\setbox0=\hbox{$3$}%
\advance\dimen0-\wd0%
\advance\dimen2\dimen8%
\dimen4=\wd0%
\hbox to0pt{\kern\dimen0\raise\dimen2\box0\hss}%
\kern\dimen6%
}
$}
\box35 \;\;=\;\; \box34 \;\;=\;\; \box33 \;\;=\;\; \box32
\endgroup
\]
[/lang]
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