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Title:  On the  Cubic Fermat Equation

Abstract: Fermat's Last Theorem, proposed by Pierre de Fermat in the 17th century, asserts that for an integer n >2,  there does not exist positive integers a, b, and c  satisfying the relation a^n + b^n = c^n. This statement remained unsolved for over 350 years, until it was finally proved by Andrew Wiles in 1994, using results in number theory, algebra, algebraic geometry, and complex analysis. The problem had stimulated much mathematical developments in the nineteenth and twentieth centuries. The case n=3 was first proved by Euler during the middle of the 18th century, but the proof he presented in 1770 in his book Algebra has an error. In this talk we shall present a proof of Fermat's Last Theorem for the case n=3, using the concept of Unique Factorisation Domain and the ring Z[w], where w is a primitive cube root of unity.