##  [Fermat's Little Theorem](/fermats-little-theorem) 

  ##  [Fermat's Little Theorem](https://natural.quantumdictionary.io/fermats-little-theorem-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A number-theoretic statement that for a prime p and integer a, a^p ≡ a (mod p); equivalently, if a is not divisible by p then a^(p-1) ≡ 1 (mod p).

 

 

 

 

 





 

 



 ##  [Fermat's Little Theorem](https://mathlogic.quantumdictionary.io/fermats-little-theorem-1) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A basic theorem in elementary number theory which asserts that for a prime p and integer a with p not dividing a, one has a^{p-1} ≡ 1 (mod p); equivalently a^p ≡ a (mod p) for all integers a.

 

 

 

 

 





 

 



 ##  [Fermat's Little Theorem](https://puremath.quantumdictionary.io/fermats-little-theorem-2) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

If p is prime and a is an integer not divisible by p, then a^{p-1} ≡ 1 (mod p); equivalently, for all integers a one has a^p ≡ a (mod p).

 

 

 

 

 





 

 



 ##  [Fermat's Little Theorem](https://algebra.quantumdictionary.io/fermats-little-theorem-3) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A number-theoretic statement that if p is prime and a is an integer not divisible by p, then a^{p−1} ≡ 1 (mod p); equivalently a^p ≡ a (mod p) for all integers a.