Rudimental Tetration

Number Theory Level 4

\[ \large 2011^{2011^{2012}} \]

If the above number is in the form of \(x^x\) for some positve integer \(x\), how many positive factors does \(x\) have (inclusive of \(1\) and itself)?

Details and Assumptions

  • No computational aids is required in solving this problem.

  • You may use the fact that \(2011\) is prime.

Image Credit: Wikimedia TetrationConvergence

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