MENTAL MODEL · M6261

Fermat's Little Theorem

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Version 1.0.0 · Updated 2026-07-28

CORE DEFINITION

Fermat's little theorem is a theorem in number theory. If a is an integer and p is a prime number, then a^p - a is a multiple of p, which can be expressed as a^p ≡ a (mod p). If a is not divisible by p, then a^(p-1) ≡ 1 (mod p).

SCAFFOLDING EFFECT

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Fermat's little theorem is a theorem in number theory. If a is an integer and p is a prime number, then a^p - a is a multiple of p, which can be expressed as a^p ≡ a (mod p).

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Fermat's little theorem states: if p is prime and a is not divisible by p, then a^(p−1) ≡ 1 (mod p). It connects modular exponentiation with prime properties and is one of the number-theoretic foundations of modern public-key cryptography (e.g., RSA).

MINIMUM ACTION

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Practice this model in one real situation:

Verify that the modulus p is prime and that the base a is coprime to p. Compute a^(p−1) mod p, which should yield 1. It is used for primality testing and modular inverse computation.

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Source support: Explicit

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zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E8%B4%B9%E9%A9%AC%E5%B0%8F%E5%AE%9A%E7%90%86ZH · Explicit
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