First Case of Fermat’s Last Theorem
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Fermat’s Last Theorem (FLT) states that $x^n+y^n=z^n$ has no non-trivial integer solution for $n>2$. It is easy to show that if the theorem is true when $n$ equals some integer $r$, then it is true when $n$ equals any multiple of $r$. Since every integer greater than 2 is divisible by 4 or an odd prime, it is sufficient to prove the theorem for $n=4$ and every odd prime. On $19^{th}$ September 1994, Andrew Wiles announced that he had finally completed the proof of FLT. In this seminar we saw an elementary proof by Sophie Germain (1823) which can be extended to prove FLT for all prime exponents less than 1700.