Fermat's Last Theorem for the Case n = 3

Abstract

Fermat's Last Theorem is one of the most difficult and famous problems in mathematics which was unsolved for more than 350 years. Fermat himself proved the theorem for the case n = 4 . Leonardo Euler gave the proof for the first odd prime number 3. Bul his proof was not complete. It contained a fallacious argument which he didn't recognize. To correct it by the most direct method, that of supplying an alternative proof of the statement for which Euler's proof is fallacious is not at all simple. Here in this paper we show how the proof can be corrected in a less direct way by bringing in arguments which Euler used to prove other propositions of Fermat. Thus we get a complete proof of the theorem for the case n = 3