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Number Theory Level 3

If the number \(9967^{9967^{9968}} \) can be represented in the form of \(x^{x}\) for some positive integer \(x\), how many positive factors does \(x\) have (inclusive of 1 and itself)?

Details and Assumptions:

  • You may use the fact that 9967 is a prime.

This problem is inspired by Anik Mandal.

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