gen-state-fermat-s-little-theorem-precisely-and-explain-why-it-m-ecf7

State Fermat's little theorem precisely and explain why it matters in 2-3 sentences.

## Fermat's Little Theorem **Statement:** If *p* is prime and *a* is any integer not divisible by *p*, then *a*^(*p*-1) ≡ 1 (mod *p*). Equivalently: For any integer *a* and prime *p*, we have *a*^*p* ≡ *a* (mod *p*). ## Why It Matters Fermat's Little Theorem is fundamental to modern cryptography, particularly RSA encryption, which secures most internet communications. It also provides efficient methods for modular exponentiation and primality testing, making it essential for computational number theory. Beyond applications, it's a cornerstone result connecting prime numbers to modular arithmetic.