Fermat's Little Theorem Calculator
Must be a positive integer
Must be a prime number
Result
How to Use
- Enter a base number (a)
- Enter a prime number (p)
- Click "Calculate" to see the result
- The calculator will verify the theorem and show the calculation steps
What is Fermat's Little Theorem?
Fermat's Little Theorem states that if p is a prime number and a is any integer not divisible by p, then:
a^(p-1) ≡ 1 (mod p)
Example: For a = 2 and p = 5:
2^(5-1) = 2^4 = 16 ≡ 1 (mod 5)
Properties and Applications
| Property | Description | Application |
|---|---|---|
| Modular Exponentiation | a^(p-1) ≡ 1 (mod p) | Fast exponentiation |
| Prime Testing | If a^(p-1) ≢ 1 (mod p), then p is not prime | Probabilistic primality testing |
| Modular Multiplicative Inverse | a^(p-2) ≡ a^(-1) (mod p) | Finding modular inverses |
Applications
- Cryptography (RSA algorithm)
- Primality testing
- Modular arithmetic calculations
- Number theory problems
- Fast exponentiation algorithms
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