Solving the Fermat and Fibonacci Equations with the Lambert-Tsallis Wq Function
Abstract
In this work, the Lambert-Tsallis Wq function is used to provide analytical solutions of fractional polynomials of the type axr+bxs+c = 0. This class of fractional polynomial appears in several areas of physics as well it is in the heart of some famous mathematical problems, like the Fermat and Fibonacci equations. Therefore, analytical solutions for the equations Ax + Bx = Cx and q1x-q2x=ysqrt(5), where q1=(1+sqrt(5))/2 and q2=(sqrt(5)-1))/2, are also provided.
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