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matqkks
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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.
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.
Fermat's Little Theorem is a mathematical theorem that states that if p is a prime number, then for any integer a, a raised to the power of p minus 1 is congruent to 1 modulo p.
Pierre de Fermat, a French lawyer and mathematician, is credited with discovering Fermat's Little Theorem in the 17th century.
Fermat's Little Theorem is significant because it provides a way to quickly determine if a number is prime. It also has applications in cryptography and number theory.
Fermat's Little Theorem is used in cryptography to ensure the security of public key encryption systems. It is also used in primality testing algorithms to efficiently determine if a number is prime.
Yes, there are limitations to Fermat's Little Theorem. It can only be applied to prime numbers, and there are rare cases where it may not hold true. Additionally, it does not provide a way to find the actual prime factors of a number.