It is false that any finite Sidon set can be embedded in a perfect
difference set modulo `p^2 + p + 1` for some prime power `p`.
As described in [arxiv/2510.19804], a counterexample is provided in [Ha47], see below.
The proof of this has been formalized.
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theorem erdos_707.variants.prime_power : (∀ (A : Set ℕ) (h : A.Finite), IsSidon A →
∃ (B : Set ℕ) (p : ℕ), IsPrimePow p ∧ A ⊆ B ∧
IsPerfectDifferenceSet B (p^2 + p + 1)) ↔ False
