Theorems · Theorem · number theory
ZMod.isSquare_neg_one_of_dvd
∀ {m n : ℕ}, m ∣ n → IsSquare (-1) → IsSquare (-1)If -1 is a square modulo n and m divides n, then -1 is also a square modulo m.
- Defined in
- Mathlib.NumberTheory.SumTwoSquares
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomproof · cited by 10,189
- ZModstatement and proof · cited by 1,024
- map_oneproof · cited by 861
- map_negproof · cited by 378
- IsSquarestatement and proof · cited by 132
- ZMod.castHomproof · cited by 55
- IsSquare.mapproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Nat.eq_sq_add_sq_of_isSquare_mod_neg_oneproof · cited by 1
- Nat.mod_four_ne_three_of_mem_primeFactors_of_isSquare_neg_oneproof · cited by 1