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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