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number_theory.​sum_four_squares

number_theory.​sum_four_squares

source
int.​exists_sum_two_squares_add_one_eq_k
int.​sum_two_squares_of_two_mul_sum_two_squares
nat.​sum_four_squares
source
theorem int.​sum_two_squares_of_two_mul_sum_two_squares {m x y : ℤ} :
2 * m = x ^ 2 + y ^ 2 → m = ((x - y) / 2) ^ 2 + ((x + y) / 2) ^ 2

source
theorem int.​exists_sum_two_squares_add_one_eq_k (p : ℕ) [hp : fact (nat.prime p)] :
∃ (a b : ℤ) (k : ℕ), a ^ 2 + b ^ 2 + 1 = ↑k * ↑p ∧ k < p

source
theorem nat.​sum_four_squares (n : ℕ) :
∃ (a b c d : ℕ), a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = n

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