Geodesic
A combinatorial proof of Euler–Fermat's theorem on presentation of primes of the form $p=8k+3$ by the quadratic form $x^2+2y^2$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 155-157 
A. I. Generalov. A combinatorial proof of Euler–Fermat's theorem on presentation of primes of the form $p=8k+3$ by the quadratic form $x^2+2y^2$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 155-157. http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a7/
@article{ZNSL_2006_330_a7,
     author = {A. I. Generalov},
     title = {A combinatorial proof of {Euler{\textendash}Fermat's} theorem on presentation of primes of the form $p=8k+3$ by the quadratic form $x^2+2y^2$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {155--157},
     year = {2006},
     volume = {330},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a7/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

An elementary and extremely short proof of the theorem on presentation of primes of the form $p=8k+3$ by the quadratic form $x^2+2y^2$ with integers $x,y$.

[1] D. Zagier, “A one-sentence proof that every prime $p\equiv 1 (\operatorname{mod}4)$ is a sum of two squares”, Amer. Math. Monthly, 97:2 (1990), 144 | DOI | MR | Zbl