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Try doing some basic maths questions in the Lean Theorem Prover. Functions, real numbers, equivalence relations and groups. Click on README.md and then on "Open in CoCalc with one click".
Project: Xena
Views: 18536License: APACHE
/-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Chris Hughes
-/
import data.zsqrtd.gaussian_int
/-!
# Sums of two squares
Proof of Fermat's theorem on the sum of two squares. Every prime congruent to 1 mod 4 is the sum
of two squares
-/
open gaussian_int principal_ideal_domain
namespace nat
namespace prime
/-- Fermat's theorem on the sum of two squares. Every prime congruent to 1 mod 4 is the sum
of two squares -/
lemma sum_two_squares {p : ℕ} (hp : p.prime) (hp1 : p % 4 = 1) :
∃ a b : ℕ, a ^ 2 + b ^ 2 = p :=
sum_two_squares_of_nat_prime_of_not_irreducible hp
(by rw [irreducible_iff_prime, prime_iff_mod_four_eq_three_of_nat_prime hp, hp1]; norm_num)
end prime
end nat