Are Fermat's Little Theorem and Wilson's Theorem Useful in Number Theory?

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SUMMARY

Fermat's Little Theorem (FLT) is highly efficient for large numbers, particularly through the use of modular exponentiation, and has significant applications in primality testing, specifically in the Fermat primality test. In contrast, Wilson's Theorem has limited practical applications, primarily serving analytic purposes rather than computational efficiency. While FLT is valuable for big modulo reductions and theorem proving, Wilson's Theorem does not offer substantial utility in finding prime numbers.

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What use are Fermat’s Little Theorem and Wilson’s theorems in number theory? Do these theorems have any real life applications? We cannot use them to find primes as both are pretty inefficient for large numbers.
 
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matqkks said:
What use are Fermat’s Little Theorem and Wilson’s theorems in number theory? Do these theorems have any real life applications? We cannot use them to find primes as both are pretty inefficient for large numbers.

FLT is pretty *damn* efficient for large numbers, look up modular exponentiation. I agree about Wilson's, though, I don't think there are too many applications to it, but FLT certainly has applications in primality testing (aka the Fermat primality test, which essentially is about applying the FLT to possible primes using random bases) and in theorem proving.
 
FlT is generally useful in big modulo reductions; some theoretical use can also be found, like FLT for n = 5. Wilson's theorem doesn't have a whole lot of applications, but they are generally used for analytic purposes.
 
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