# Ridiculous Bases!

Number Theory Level pending

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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