     
\documentclass[addpoints]{exam}
    


\usepackage{amsfonts}
\usepackage{amsmath}
\sloppy


\begin{document}

  \pagestyle{headandfoot}
  \runningheadrule
  \firstpageheader{ Math 15A }{ Homework 6 }{ March 8, 2019 }
  \runningheader{ Math 15A }{ Homework 6, Page \thepage\ of \numpages}{ March 8, 2019 }

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  \begin{flushright}
    \makebox[0.4\textwidth]{Name: \enspace\hrulefill}

    \vspace{0.2in}
    \makebox[0.4\textwidth]{Pid:\enspace\hrulefill}
  \end{flushright}

  \begin{questions}
    \question[10]
      Let $n$ be a positive integer. Show that in any set of $n$ consecutive integers
			there is at least one divisible by $n$.

      \begin{solution}[\stretch{1}]
      \end{solution}
      \newpage
    \question
      Prove that for every integers $a_1$, \dots, $a_n$ there are
			$k > 0$ and $\ell \ge 0$ such that $k + \ell \le n$ and
			$\sum\limits_{i = k}^{k + \ell} a_i$ is divisible by $n$.

      \begin{solution}[\stretch{1}]
      \end{solution}
      \newpage
  \end{questions}
\end{document}