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This is a Quantitative Study study.

October 16, 2025Open Access

Sums of squares of integers except for a fixed one

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This approach determines the minimum number of squares of integers needed to represent positive integers excluding a fixed integer.
Key findings show that all positive integers can be expressed as sums of squares except for a specific integer, enhancing classical results.
The study generalizes Dubouis's result, particularly addressing cases when the excluded integer is zero.
It provides a deeper understanding of integer representations in the context of sum of squares.

Implication

This study finds minimum sums of squares excluding a fixed integer, suggesting new insights in number theory.

Abstract

In this article, we study a sum of squares of integers except for a fixed one. For any nonnegative integer n, we find the minimum number of squares of integers except for n whose sums represent all positive integers that are represented by a sum of squares except for it. This problem could be considered as a generalization of Dubouis's result for the case when $n=0$.

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Cite This Study

Chae et al. (2025) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fcfd1 https://doi.org/10.48550/arxiv.2504.03467

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Implication

This study finds minimum sums of squares excluding a fixed integer, suggesting new insights in number theory.

Sums of squares of integers except for a fixed one

Key Points

Implication

Abstract

Discussion

Cite This Study

Sums of squares of integers except for a fixed one

Key Points

Implication

Abstract

Discussion

Cite This Study

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