An Alternate Simple Proof of Fermat’s Last Theorem

Abstract

â„œ denotes the real line as well as the set of all real numbers, and the real numbers are considered as if they are points on the real line, and the points on the real line as if they are real numbers. Hence, three positive rational numbers a, b & c, satisfying the condition cⁿ = aⁿ + bⁿ, where abc ≠ 0, and n is an integer greater than 1, will represent three sides of a triangle, say ΔABC, on a two dimensional plane. Consequently, the algebraic equation will yield the trigonometric equation SinⁿA + SinⁿB = Sinⁿ(A+B). The solution of this equation, in general, will be in the form of B = f(A), where the relation between the variables A & B has to be linear in nature on account of the properties of the ΔABC, which is on a two dimensional plane with the relation between the vertical angles given by (A+B+C) = Ï€, as well as the exponent of the variables A & B of the trigonometric equation is also one; but this condition is satisfied only when n = 2. Hence, the algebraic equation has rational solutions only with n = 2 and the FLT is true.