What question did this study set out to answer?

This investigation seeks to confirm Sun Zhiwei's conjecture regarding the representation of non-negative integers using specific binomial coefficients.

July 26, 2026Open Access

A Computational and Analytic Investigation of Sun's (2-4-6-8) Binomial Representation Conjecture: Asymptotic Evidence, Local Theory, and Limitations

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SSScott Sun

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Implication

Computational verification and local theory support the conjecture in non-negative integers, suggesting future exploration is needed.

Key Points

This investigation seeks to confirm Sun Zhiwei's conjecture regarding the representation of non-negative integers using specific binomial coefficients.
Computational verification for integers up to 1,000,000 to establish the number of representations.
Analysis of local solubility conditions across various moduli.
Development of a Hardy–Littlewood circle method framework to study polynomial contributions.
The conjecture holds for all integers 1 to 1,000,000, with at least 2 representations for each integer.
Local solubility confirmed for multiple moduli, indicating no obstructions to the conjecture.
Minor arc contributions pose challenges for proving the full conjecture for large integers.

Cite This Study

Scott Sun (2026) studied this question.

synapsesocial.com/papers/6a65a306d3aea3239cd76552 https://doi.org/10.5281/zenodo.21505247

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A Computational and Analytic Investigation of Sun's (2-4-6-8) Binomial Representation Conjecture: Asymptotic Evidence, Local Theory, and Limitations

Discussion

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Implication

Key Points

Cite This Study

A Computational and Analytic Investigation of Sun's (2-4-6-8) Binomial Representation Conjecture: Asymptotic Evidence, Local Theory, and Limitations

Discussion

Member takes

Implication

Key Points

Cite This Study

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