Jacobi's theorem is: the number of ways of representing $N$ as a sum of two squares is $4(d_1(N)-d_3(N))$ where $d_i(N)$ is the number of divisors of $N$ that are of the form $4k+i$. I was wondering if there is a combinatorial proof of this (involving, of course, the divisors of $N$). I am working on such a proof but don't want to repeat others' work.

Démonstration de la conjecture de Dumont, math.univ-lyon1.fr/~lass/articles/pub13dumontj.pdf . But I'm not sure if you count this proof as combinatorial. $\endgroup$ – darij grinberg Aug 17 '17 at 16:30Satin squaresand the movement at the time to write about mathematics for general audiences. $\endgroup$ – Brian Hopkins Aug 18 '17 at 13:36