All open problems
Source labels openChecked July 26, 2026

WikipediaNumber theory

Magic Squares

Does there exist a 3×33 \times 3 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 3×33 \times 3 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

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem exists_magic_square_squares :    answer(sorry)   m : Fin 3  Fin 3  ,  t : ,       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