FormalConjectures.Mathoverflow.«21003»

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import FormalConjecturesUtil

Mathoverflow 21003

Is there any polynomial $f(x, y) \in \mathbb{Q}[x, y]$ such that $f : \mathbb{Q} \times \mathbb{Q} \rightarrow \mathbb{Q}$ is a bijection?

Reference: mathoverflow/21003 asked by user Z.H.


open scoped Polynomial



namespace Mathoverflow21003

Is there any polynomial $f(x, y) \in \mathbb{Q}[x, y]$ such that $f : \mathbb{Q} \times \mathbb{Q} \rightarrow \mathbb{Q}$ is a bijection?

@[category research open, AMS 12]
theorem declaration uses 'sorry'mathoverflow_21003 :
    answer(sorry) ↔ ∃ f : MvPolynomial (Fin 2) ℚ, Function.Bijective fun x ↦ f.eval x := by⊢ True ↔ ∃ f, Function.Bijective fun x => (MvPolynomial.eval x) f
  sorryAll goals completed! 🐙


end Mathoverflow21003