where \(a = b\,\textrm{mod }c\):
\[ ad = bd\,\textrm{mod }cd \]
\[ \frac{a}{d} = \frac{b}{d}\,\textrm{mod }\frac{c}{d} \]
where \(p\) is a prime and \(a\) is any integer
\[ a^{p} = a\,\textrm{mod }p \]