Fermat's Little Theorem Calculator
Understanding Fermat's Little Theorem
Fermat's Little Theorem is a fundamental result in number theory that describes a property of prime numbers.
The Theorem:
If \(p\) is a prime number, then for any integer \(a\), the number \(a^p - a\) is an integer multiple of \(p\). In the notation of modular arithmetic, this is expressed as:
\( a^p \equiv a \pmod{p} \)
An alternative form of the theorem states that if \(p\) is a prime and \(a\) is an integer not divisible by \(p\), then:
\( a^{p-1} \equiv 1 \pmod{p} \)
Disclaimer: This calculator is for educational purposes only. While we strive for accuracy, please verify all results for critical applications.
Verifies that \(a^p \equiv a \pmod{p}\) for a prime p.
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