erdos_477

Is there a polynomial $f:\mathbb{Z}\to \mathbb{Z}$ of degree at least $2$ and a set $A\subset \mathbb{Z}$ such that for any $z\in \mathbb{Z}$ there is exactly one $a\in A$ and $b\in \{ f(n) : n\in\mathbb{Z}\}$ such that $z=a+b$?

theorem erdos_477 : answer(sorry) ↔
    ∃ f : ℤ[X], 2 ≤ f.degree ∧ ∃ A : Set ℤ,
      ∀ z, ∃! ab ∈ A ×ˢ (f.eval '' {n | 0 < n}), z = ab.1 + ab.2

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