Ridiculous Bases!

What is $(31^2)_n$ ?

Where, $n = \binom{m}{13}$ and $m = \binom{82}{54}$

Please provide your answer in base $n$ , not decimal.

Clarification: The subscript means base $n$ , and the notation $\binom{a}{b}$ indicates " $a$ choose $b$ " or the binomial coefficient indexed by $a$ and $b$ .

Hint: Although this problem appears to be compute intensive, in reality it is not... Good luck!

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