This theorem states that for any n except 2, the equation X^n+Y^n=Z^n is not true for any positive integer triplet X, Y and Z. Fermat's "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain." has fascinated mathematicians from 1637 but no one has found what his proof was. Let us try to understand this theorem better.

Please read the article at 
On Fermat's last theorem 
http://pengkuanonmaths.blogspot.com/2015/07/on-fermats-last-theorem.html
or On Fermat's last theorem
https://www.academia.edu/13665056/On_Fermat_s_last_theorem