One Two Three Four Five Six Seven

Number Theory Level pending

Note that

\[ \LARGE 1 = 2^{3^{4^{5^6}}} \bmod 7 \]

What is the smallest positive integer \(n>7\) such that

\[ \LARGE 1 = 2^{3^{4^{.^{.^{.^{n-1}}}}}} \bmod {n} \]

is also true?

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