Magic Squares
Does there exist a matrix such that every entry is a distinct square, and all rows, columns, and diagonals add up to the same value?
Mathematical statement
Does there exist a matrix such that every entry is a distinct square, and all rows, columns, and diagonals add up to the same value?
0 is excluded, as a Magic Square of Squares with 0 and 8 distinct squares is know is knownn. See Magic Square of Squares
Statement source: Wikipedia statement material
Statement terms: Source-specific
Source-specific terms. Therefore does not assert reuse rights beyond attributed display.
Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
exists_magic_square_squares
theorem exists_magic_square_squares : answer(sorry) ↔ ∃ m : Fin 3 → Fin 3 → ℕ, ∃ t : ℕ, m.Injective2 ∧ (∀ i j, 0 < (m i j) ∧ IsSquare (m i j)) ∧ (∀ i, ∑ j, m i j = t) ∧ (∀ j, ∑ i, m i j = t) ∧ m 0 0 + m 1 1 + m 2 2 = t ∧ m 0 2 + m 1 1 + m 2 0 = t := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References