green_60

Is there an absolute constant $c > 0$ such that, whenever $A ⊆ \mathbb{N}$ is a set of squares with $|A| ≥ 2$, the sumset $A + A$ satisfies $|A + A| ≥ |A|^{1 + c}$?

theorem green_60 :
    answer(sorry) ↔ ∃ c > (0 : ℝ),
      ∀ (A : Finset ℕ),
        (∀ a ∈ A, IsSquare a) →
        2 ≤ A.card →
          ((A + A).card : ℝ) ≥ (A.card : ℝ) ^ (1 + c)

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