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Where is the Wilson theoreme used? I've recently learned…

Where is the Wilson theoreme used?

I've recently learned Wilson's Theorem and its proof.

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I'd like to know what kinds of patterns or clues in a problem should make me think of Wilson's Theorem.

For example, are there certain types of congruences, factorial expressions primerelated conditions, product modulo a prime, or other recurring situations where experienced problem solvers immediately consider Wilson's Theorem

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In general, what features of a problem suggest that Wilson's Theorem might be useful even if the theorem is not explicitly mentioned?

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Or there isn't problems who is really need this Theorem because I think is kinda useless

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