Das ternäre Goldbach-Problem mit Einschränkungen an die Summanden.
Let Sq denote the set of squares, and let be the squaring function restricted to powers of n; let ⊥ denote the coprimeness relation. Let . For every integer n ≥ 2 addition and multiplication are definable in the structures ⟨ℕ; Bn,⊥⟩ and ⟨ℕ; Bn,Sq⟩; thus their elementary theories are undecidable. On the other hand, for every prime p the elementary theory of ⟨ℕ; Bp,SQp⟩ is decidable.