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It is well known that the representation number of sum of three squares is related to the (form) class number of binary quadratic forms, which was proved by Gauss.

But, I could not find references to explain his motivation for this relation.

I appreciate if you teach me how Gauss recognized the relation.

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  • $\begingroup$ see mathoverflow.net/questions/3596/… $\endgroup$
    – Will Jagy
    Jan 30, 2022 at 2:34
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    $\begingroup$ seems the reference you want is Grosswald, Representations of Integers as Sums of Squares (1985) $\endgroup$
    – Will Jagy
    Jan 30, 2022 at 2:54
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    $\begingroup$ See also this post here, with many links and the answer by Franz Lemmermeyer. $\endgroup$ Jan 30, 2022 at 12:10

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