In 1994 the mathematician Andrews Wiles proved, using concepts of modern mathematics, namelythe Modular Elliptic Curves, the Fermat's Last Theorem. That demonstration is long and it isunderstandable to mathematic specialists, moreover, these mathematical concepts were not knownat the time when Fermat lived, so he could not prove it throug this road. I thought that there mightbe another simpler proof which would use the properties of algebraic equations and inequalities.These mathematical concepts were known at the time in which Fermat lived and which, therefore,could apply for the proof of the theorem of which he wrote, in the margin of a page of the book ofArithmetica of Diophantus he was reading, to have found a demonstration "wonderful," but that hehad not could to write to the narrowness of the margin itself. I propose, therefore, the followingdemonstration that directly uses the mathematical properties of algebraic equations and inequalitiesthat are understood by all those who study algebra.