What does this research mean for the field?

The Schinzel-Sierpiński conjecture for 5/n can be strictly reduced to prime denominators and explicitly solved for specific residue classes and small primes, with all derivations and solutions formally verified in Lean 4. Novelty: ClaimNovelty.CONFIRMATORY. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Investigate the Schinzel-Sierpiński conjecture on Egyptian fractions for the specific case of 5/n, assessing whether it can be decomposed into a sum of three unit fractions for all positive denominators.

August 29, 2026Open Access

Generalized Erdős-Straus and Schinzel-Sierpiński Conjectures

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Authors

CNCharles EDOU NZE

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Implication

Mathematical analysis demonstrates parametric decompositions for Sierpiński's conjecture in prime denominators, indicating the validity of generalized Egyptian fraction representations.

Key Points

Investigate the Schinzel-Sierpiński conjecture on Egyptian fractions for the specific case of 5/n, assessing whether it can be decomposed into a sum of three unit fractions for all positive denominators.
Derived algebraic parametric families covering residue classes modulo 5, modulo 4, and modulo 20 to provide explicit unit fraction triples.
Utilized the Elsholtz-Tao analytic framework and Bombieri-Vinogradov sieve methods to bound representation counts and analyze exceptional prime sets.
Formally certified rational fraction identities, field simplifications, and parametric solutions with zero axioms and zero sorries using the Lean 4 interactive theorem prover and Mathlib.
Proved a global prime reduction demonstrating that any valid decomposition for 5/p directly scales to composite denominators n = p · m.
Exhaustively enumerated and verified explicit integer solutions (x, y, z) for all 25 prime denominators p ≤ 100.
Confirmed through sieve analytic methods that the asymptotic density of exceptional prime denominators failing the decomposition is zero.

Cite This Study

Charles EDOU NZE (2026) studied this question.

synapsesocial.com/papers/6a9299958e5d7d1fc0c11989 https://doi.org/10.5281/zenodo.22133032

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Implication

Mathematical analysis demonstrates parametric decompositions for Sierpiński's conjecture in prime denominators, indicating the validity of generalized Egyptian fraction representations.

Generalized Erdős-Straus and Schinzel-Sierpiński Conjectures

Discussion

Member takes

Implication

Key Points

Cite This Study

Generalized Erdős-Straus and Schinzel-Sierpiński Conjectures

Discussion

Member takes

Implication

Key Points

Cite This Study

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