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arXiv · 1707.01772

Elementary proof of Fermat's Last Theorem for even exponents

Anatoly A. Grinberg
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Abstract

A elementary proof of Fermat"s Last Theorem[1] is presented for the case of even exponents n=2q, where q is any integer, including 2. For even exponents, the proof of the theorem reduces to showing that solutions of the Pythagorean equation X_p,Y_p,Z_p are impossible to equate q-th powers X^q,Y^q,Z^q of Fermat"s equation solutions. In other words, Fermat"s equation with even exponents does not have a solution, due to the impossibility of extracting the q-th root from corresponding numbers X_p,Y_p,Z_p of the Pythagorean equation solutions. Similarly to Fermat"s proof for the case, n=4, the simplicity of the approach used here is based on the use of the Pythagorean equation solution.

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Anatoly A. Grinberg. 2017-07-05. Elementary proof of Fermat's Last Theorem for even exponents. https://arxiv.org/abs/1707.01772

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