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%%  An UIT Edition example
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%%  Example 10-06-3 on page 209.
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%%  Copyright (C) 2010 Herbert Voss
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\documentclass[]{exaarticle}
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\StartShownPreambleCommands
\usepackage{amsmath}
\let\dst\displaystyle
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\begin{document}
\[ \binom{n}{k} = \dfrac{\dst\prod_{i=1}^n i}
  {\dst\prod_{i=1}^k i\dst\prod_{i=1}^{n-k} i} \]
The Euclidean algorithm: if $a>b$ are integers then $\gcd(a,b)=\gcd(a\bmod b,b)$.
If $\prod_{i=1}^n p^{e_i}_i$ is the prime factorization of $x$ then
\[ S(x)=\sum_{d\vert x}d=\prod_{i=1}^n{p^{e_i+1}_i-1\over p_i-1}. \]
\end{document}
