On a Conjecture of Sun about sums of restricted squares

Soumyarup Banerjee

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arXiv · 2202.04057

On a Conjecture of Sun about sums of restricted squares

Soumyarup Banerjee

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Abstract

In this paper, we investigate sums of four squares of integers whose prime factorizations are restricted, making progress towards a conjecture of Sun that states that two of the integers may be restricted to the forms $2^a3^b$ and $2^c5^d$. We obtain an ineffective generalization of results of Gauss and Legendre on sums of three squares and an effective generalization of Lagrange's four-square theorem.

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Soumyarup Banerjee. 2022-02-08. On a Conjecture of Sun about sums of restricted squares. https://arxiv.org/abs/2202.04057

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