October 1, 2025Open Access

Note on the sumset of squares

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The result shows that for any finite subset of square numbers, the size of the sumset is significantly large.
The lower bound derived is |Q+Q| ≥ C'|Q| (log |Q|)^{1/3+o(1)}, providing insight into the distribution of square numbers.
Tools similar to those used by Mei-Chu Chang were applied to achieve this result, indicating a methodological consistency in the field.
The author intends to withdraw the ArXiv paper as the findings closely mirror those published previously.

Implication

This proof identifies lower bounds on the size of sumsets in finite subsets of square numbers, suggesting implications for number theory.

Abstract

It is proved that for any non-empty finite subset Q of the square numbers, |Q+Q|≥ C'|Q|(log |Q|)1/3+o(1). This result essentially is proved -- with the same tools -- by Mei-Chu Chang. See in J. Funct. Anal. 207 (2004), no 2, 444-460. So the author will withdraw this ArXiv file.

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Norbert Hegyvári (2025) studied this question.

synapsesocial.com/papers/68dd89defe798ba2fc497da3 https://doi.org/10.48550/arxiv.2504.13230

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Implication

This proof identifies lower bounds on the size of sumsets in finite subsets of square numbers, suggesting implications for number theory.

Note on the sumset of squares

Key Points

Implication

Abstract

Discussion

Cite This Study

Note on the sumset of squares

Key Points

Implication

Abstract

Discussion

Cite This Study

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