# Number TheoryFermat's Little Theorem

#### matqkks

##### Member
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.

#### Bacterius

##### Well-known member
MHB Math Helper
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.

#### mathbalarka

##### Well-known member
MHB Math Helper
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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