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{\bf Solution.} #1

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\vspace{-3cm}




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\newtheorem{theorem}{Theorem}
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\begin{document}

\toptop

\noindent
\begin{theorem}
Let $p$ be a prime and $k$ be a natural number.  Prove that:\\
(a) $k$ divides the product of $k$ consecutive integers. (recall, we offered an elegant solution of this in the past...)\\
(b) For each $n\in \mathbb{N}$, $(1+n^p) = (1+n)^p mod p$
\end{theorem}





















\end{document}










