\( \newcommand{\combin}[2]{{}^{#1}C_{#2} } \newcommand{\cmod}[3]{#1 \equiv #2\left(\bmod {}{#3}\right)} \newcommand{\mdc}[2]{\left( {#1},{#2}\right)} \newcommand{\mmc}[2]{\left[ {#1},{#2}\right]} \newcommand{\cis}{\mathop{\rm cis}} \newcommand{\sen}{\mathop{\rm sen}} \newcommand{\senq}{\mathop{\rm sen^2}} \newcommand{\tg}{\mathop{\rm tg}} \newcommand{\cotg}{\mathop{\rm cotg}} \newcommand{\cotgh}{\mathop{\rm cotgh}} \newcommand{\tgq}{\mathop{\rm tg^2}} \newcommand{\cotgq}{\mathop{\rm cotg^2}} \newcommand{\cotghq}{\mathop{\rm cotgh^2}} \newcommand{\cosec}{\mathop{\rm cosec}} \newcommand{\cosech}{\mathop{\rm cosech}} \newcommand{\cosecq}{\mathop{\rm cosec^2}} \newcommand{\cosechq}{\mathop{\rm cosech^2}} \newcommand{\sh}{\mathop{\rm sh}} \newcommand{\shq}{\mathop{\rm sh^2}} \newcommand{\ch}{\mathop{\rm ch}} \newcommand{\chq}{\mathop{\rm ch^2}} \newcommand{\argsh}{\mathop{\rm argsh}} \newcommand{\argch}{\mathop{\rm argch}} \newcommand{\arctg}{\mathop{\rm arctg}} \newcommand{\vect}[1]{\overrightarrow{#1}} \newcommand{\tr}[1]{ \textnormal{Tr}\left({#1}\right)} \newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\R}{\mathbb{R}} \newcommand{\C}{\mathbb{C}} \newcommand{\H}{\mathbb{H}} \newcommand{\vect}[1]{\overrightarrow{#1}} \newcommand{\Mod}[1]{\ (\mathrm{mod}\ #1)} \)

14/03/2017

O resto de uma divisão...

Hoje vou apresentar uma resolução feita num intervalo, esboçada num recibo de café...com mais algum detalhe que o recibo.

Problema: Qual é o resto da divisão de $\underbrace {2323 ... 232323}_{\text{$4018$ dígitos}}$   por $999$?

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