, Volume 82, Issue 3-4, pp 352-356

On Euler’s hypothetical proof

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Abstract

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, from Euler’s results, one can obtain an elementary proof of the nonexistence of positive integer solutions of the equation x 3 + y 3 = z 3.

Original Russian Text © J. J. Mačys, 2007, published in Matematicheskie Zametki, 2007, Vol. 82, No. 3, pp. 395–400.