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Fermat's Little Theorem is a key result in number theory, stating that for a prime number p and an integer a not divisible by p, the expression a^(p-1) is congruent to 1 modulo p. This theorem can help in primality testing, though limitations exist, especially with certain types of composite numbers called Carmichael numbers. The chapter also delves into practical applications of the theorem in calculations and the concepts of pseudo primes and Carmichael numbers.
Chapter 1221 sections
Fermat's Little Theorem is a key result in number theory, stating that for a prime number p and an integer a not divisible by p, the expression a^(p-1) is congruent to 1 modulo p. This theorem can help in primality testing, though limitations exist, especially with certain types of composite numbers called Carmichael numbers. The chapter also delves into practical applications of the theorem in calculations and the concepts of pseudo primes and Carmichael numbers.
Fermat's Little Theorem provides a method for primality testing and modular arithmetic.
The theorem can be used to conclude properties of numbers under certain conditions but has notable exceptions.
Carmichael numbers can cause misleading results in primality testing, displaying behaviors similar to primes despite being composite.
If p is a prime number and a is an integer such that p does not divide a, then a^(p-1) ≡ 1 (mod p).
A method to determine if a number is prime, which can utilize concepts such as Fermat's Little Theorem.
Composite numbers that satisfy Fermat's Little Theorem for all bases that are coprime to the number.
A composite number n that satisfies the condition a^(n-1) ≡ 1 (mod n) for a certain integer a coprime to n.
Total Questions
2
Estimated Time
4 min
Passing Score
70%
1 more question available