I have discovered a truly remarkable proof which this margin is too small to contain.
Since he did not provide his proof, the theorem remained a conjecture for a long time and stimulated the research in number theory for decades and centuries. The conjecture was proven by Andrew Wiles only in the year 1995, using very complicated and sophisticated methods. It remains a mystery if Fermat really found a correct proof which was more simple.
No $n > 2$ is an integer, no three positive integers $a,b,c\in\mathbb Z$ satisfy the equation $$a^n+b^n=c^n.$$