A proof of Fermat's theorem on sum of two squares. It is the proof that uses gaussian integers. This is done in ssreflect. It contains two files :

gauss_int.v : the definition of gaussian integers

fermat2.v : the proof of Fermat's theorem

The final statement reads:

From mathcomp.contrib.sum_of_two_square Require Import fermat2.

Check sum2stest.

sum2stest :

reflect (forall p, prime p -> odd p -> p %| n -> odd (logn p n) -> p %% 4 = 1) (n is a sum_of_two_square).

• Author(s):
  • Laurent Théry
• License: MIT License
• Compatible Coq versions: 8.18 or later
• Additional dependencies:
  • MathComp ssreflect 2.1 or later
  • MathComp algebra 2.1 or later
  • MathComp field 2.1 or later
• Coq namespace: twoSquare
• Related publication(s): none

To build and install manually, do:

git clone https://github.com/thery/twoSquare.git
cd twoSquare
make   # or make -j <number-of-cores-on-your-machine> 
make install