My three published papers subsequently are having no error , and gives a valid elementary proof for Fermat's Last Theorem ( my research published papers are attached herewith
My final version entitled,"A Solution for Fermat's last theorem using Ramanujan-Nagell equation " has been published in European Journal of Mathematics and Statistics, Volume 4, no.6 (2023)
Also another paper entitled " A Proof for Fermat's Last Theorem " published in European Journal of Mathematics and Statistics is attached herewith.
Both papers are distinct in the sense that the second paper is not the duplication or replica of the first paper , and noone could get the idea of forming the transformation equations concept from the first one.( file enclosed)