Geodesic
On Euler's Hypothetical Proof
Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 395-400.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is conjectured that Euler possessed an elementary proof of Fermat's theorem for $n=3$. In this note, we show that this opinion is rather credible, because Euler's results can justify an elementary proof of the nonexistence theorem for nontrivial integer solutions of the equation $x^3+y^3=z^3$.
Keywords: Fermat's Last Theorem, coprime numbers. 
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J. J. Mačys. On Euler's Hypothetical Proof. Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 395-400. http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a7/

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