We give a proof of the solvability in a natural numbers for Fermat’s Last theorem and the equations ax+by=cz and Xn11 + Xn22 + ... + Xnk-1k-1 = Xnkk has not been found earlier, significantly different from known, and allow us to obtain infinite set of solutions in natural numbers, and examples.
Bulletin of Mathematical Sciences and Applications (Volume 5)
K. R. R. Gandhi and R. Tint, "The Reproductive Solution for Fermat’s Last Theorem (Elementary Aspect)", Bulletin of Mathematical Sciences and Applications, Vol. 5, pp. 5-11, 2013