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 ax^r+bx^s+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 A^x + B^x = C^x and q1^x-q2^x=ysqrt(5), where q1=(1+sqrt(5))/2 and q2=(sqrt(5)-1))/2, are also provided.