The first case of Fermat's last theorem

@article{Adleman1985TheFC,
  title={The first case of Fermat's last theorem},
  author={Leonard M. Adleman and D. R. Heath-Brown},
  journal={Inventiones mathematicae},
  year={1985},
  volume={79},
  pages={409-416}
}
Fermat’s Last Theorem (FLT) states that x + y = z has no 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 September 1994, Andrew Wiles announced that he had finally completed the proof of FLT. Today we will see an elementary proof by Sophie Germain… Expand
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References

SHOWING 1-4 OF 4 REFERENCES
The first case of fermat’s last theorem
Fermat , a r o u n d 1637, s t a ted tha t the D i o p h a n t i n e equation x n + yn = z ~ has no solutions in positive integers, if n > 2. This s tatement, which has never been p roved or dExpand
13 lectures on Fermat's last theorem
Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 OtherExpand