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moonlight310
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Homework Statement
let p be prime then, (p-1)! is congruent to -1 mod p
Homework Equations
The Attempt at a Solution
I'm not sure where to start
Fermat's Little Theorem states that if p is a prime number, then for any integer a, a^p ≡ a (mod p).
Fermat's Little Theorem can be used to prove that for any prime number p, (p-1)! ≡ -1 (mod p). This is known as Wilson's Theorem.
This theorem has many applications in number theory and cryptography. It is also used in the proof of the famous Fermat's Last Theorem.
The proof of Fermat's Little Theorem involves using mathematical induction and properties of modular arithmetic.
Yes, there is a generalization of Fermat's Little Theorem known as Euler's Theorem, which states that for any integer a and positive integer n, a^φ(n) ≡ 1 (mod n), where φ(n) is Euler's totient function.