Euler's sum of powers conjecture
Euler's sum of powers conjecture states that for integers and , if the sum of positive integers each raised to the -th power equals another integer raised to the -th power, then .
Mathematical statement
Euler's sum of powers conjecture states that for integers and , if the sum of positive integers each raised to the -th power equals another integer raised to the -th power, then .
The conjecture is known to be false for and , but remains open for .
Statement source: Wikipedia statement material
Statement terms: CC-BY-SA-4.0
Attributed source material. Reuse must follow the linked attribution and share-alike terms.
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
eulers_sum_of_powers_conjecture
theorem eulers_sum_of_powers_conjecture (n k b : ℕ) (hn : 1 < n) (hk : 5 < k) (a : Fin n → ℕ) (ha : ∀ i, a i > 0) (hsum : ∑ i, (a i) ^ k = b ^ k) : k ≤ n := 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