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Investigate the Erdős-Moser power sum Diophantine equation to determine constraints on non-trivial positive integer solutions and provide machine-checked proofs.

August 20, 2026Open Access

On the Erdős-Moser Diophantine Equation

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CNCharles EDOU NZE

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Implication

Formal mathematical analysis demonstrates modular exclusions and machine-checked bounds for the Erdős-Moser Diophantine equation, highlighting constraints on non-trivial solutions.

Key Points

Investigate the Erdős-Moser power sum Diophantine equation to determine constraints on non-trivial positive integer solutions and provide machine-checked proofs.
Evaluated continuous asymptotics by comparing discrete power sums to continuous integrals.
Formulated complete step-by-step mathematical inductions for small base cases and applied Leo Moser's modular sieve reductions.
Formally encoded and certified all exclusion proofs and inductive bounds in the Lean 4 interactive theorem prover using Mathlib with zero axioms or sorry placeholders.
Demonstrated that any hypothetical non-trivial solution must satisfy the critical diagonal asymptotic balance of m ≈ k + 1.
Established the unconditional non-existence of integer solutions for m = 4 and m = 5 across all positive integer exponents k.
Proved via modular pairing symmetries that exponent k must necessarily be an even integer (k = 2h), with 100% formal verification in Lean 4.

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Charles EDOU NZE (2026) studied this question.

synapsesocial.com/papers/6a86b57f8a91293e6a1cceae https://doi.org/10.5281/zenodo.21991882

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Implication

Formal mathematical analysis demonstrates modular exclusions and machine-checked bounds for the Erdős-Moser Diophantine equation, highlighting constraints on non-trivial solutions.

On the Erdős-Moser Diophantine Equation

Discussion

Member takes

Implication

Key Points

Cite This Study

On the Erdős-Moser Diophantine Equation

Discussion

Member takes

Implication

Key Points

Cite This Study

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