# The Last Primetime

Number Theory Level pending

$\large x^n + y^n = z^n$

All variables in this equation represent positive integers. Moreover, $$n > 1$$.

For what integral value(s) of $$n$$ does the equation have solutions?

Submit answer as sum of possible values of $$n$$, if finite solutions.

Submit $$666$$ , if no solution possible.

submit $$999$$ , if there are infinite solutions.

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