Theorems · Theorem · commutative algebra
IsCoprime.sq_add_sq_ne_zero
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a b : R},
IsCoprime a b → a ^ 2 + b ^ 2 ≠ 0- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 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.
- CommRingstatement and proof · cited by 17,173
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- IsCoprimestatement and proof · cited by 321
- sq_nonnegproof · cited by 106
- eq_zero_of_pow_eq_zeroproof · cited by 30
- add_eq_zero_iff_of_nonnegproof · cited by 8
- not_isCoprime_zero_zeroproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ModularGroup.smul_eq_lcRow0_addproof · cited by 1
- ModularGroup.tendsto_abs_re_smulproof · cited by 1