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- W4285704385 abstract "In this paper we mainly study sums of four rational squares with certain restrictions. Let $mathbb Q_{ge0}$ be the set of nonnegative rational numbers. We establish the following four-square theorem for rational numbers: For any $a,b,c,dinmathbb Q_{ge0}$, each $rinmathbb Q_{ge0}$ can be written as $x^2+y^2+z^2+w^2$ with $x,y,z,winmathbb Q_{ge0}$ such that $ax+by+cz+dw$ is a rational square (or a rational cube). This paper also contains many conjectures; for example, for any positive integers $a$ and $b$ with $gcd(a,b)=1$, we conjecture that each $rinmathbb Q_{ge0}$ can be written as $aw^4+bx^4+y^2+z^2$ with $w,x,y,zinmathbb Q$." @default.
- W4285704385 created "2022-07-18" @default.
- W4285704385 creator A5030071648 @default.
- W4285704385 date "2020-10-12" @default.
- W4285704385 modified "2023-09-27" @default.
- W4285704385 title "Sums of four rational squares with certain restrictions" @default.
- W4285704385 doi "https://doi.org/10.48550/arxiv.2010.05775" @default.
- W4285704385 hasPublicationYear "2020" @default.
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