Theorems · Theorem · number theory
PythagoreanTriple.even_odd_of_coprime
∀ {x y z : ℤ}, PythagoreanTriple x y z → x.gcd y = 1 → x % 2 = 0 ∧ y % 2 = 1 ∨ x % 2 = 1 ∧ y % 2 = 0- Defined in
- Mathlib.NumberTheory.PythagoreanTriples
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- zero_addproof · cited by 2,366
- sub_eq_iff_eq_addproof · cited by 74
- PythagoreanTriplestatement and proof · cited by 24
- Int.natCast_dvdproof · cited by 16
- exists_eq_mul_left_of_dvdproof · cited by 9
- PythagoreanTriple.eqproof · cited by 7
- Int.emod_two_eq_zero_or_oneproof · cited by 5
- Int.sq_ne_two_mod_fourproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- PythagoreanTriple.isPrimitiveClassified_of_coprime_of_posproof · cited by 1