\begin{definition}[Definition:Friedman Number]
A '''Friedman number (base $n$)''' is a (positive) integer which is the result of an expression in base $n$ arithmetic which contains exactly its digits.
The expression is subject to the following constraints:
:$(1): \quad$ The arithmetic operators $+$, $-$, $\times$, $\div$ and exponentiation are the only operators which are allowed.
:$(2): \quad$ Parentheses are allowed, but only in order to override the default operator precedence, otherwise every number would trivially be Friedman by $n = (n)$.
:$(3): \quad$ Leading zeroes are not allowed, otherwise other numbers would trivially be Friedman by, for example, $011 = 10 + 1$.
\end{definition}