# 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

#### 28 Citations

New bound for the first case of Fermat’s last theorem

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For a prime number p, the first case of Fermat’s last theorem for exponent p asserts that for any three integers x, y, z with xp+yp+zp=O at least one of x, y, z is divisible by p. In the present… Expand

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We show that if the first case of Fermat’s Last Theorem is false for prime exponent p then p2 divides qp — q for all primes q < Sq. As a corollary we state the theorem of the title. © 1988 American… Expand

The first case of fermat’s last theorem

- Mathematics
- 1985

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 d… Expand

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(1) f(x1 , x k 2 , . . . , x k n) = 0 has solutions in non-zero integers x1, x2, . . . , xn. For homogeneous diagonal f of degree one, Davenport and Lewis [DL] showed that k ∈ T (f) whenever (n − 1)… Expand

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Let C be a curve of genus g >_ 2, defined over a number field K , and let J be the Jacobian of C. Coleman [C2], following Chabauty, has shown how to obtain good bounds on the cardinality of C(K) if… Expand

Arithmetic applications of Kloosterman sums

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Last April saw the 100-th anniversary of the birth of H.D. Kloosterman. The occasion was celebrated by a one day meeting in Leiden, and this article is a report on one of the lectures given. It… Expand

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The last chapter brings a short survey on the work on Fermat’s Last Theorem, culminating in its proof.

#### References

SHOWING 1-4 OF 4 REFERENCES

The first case of fermat’s last theorem

- Mathematics
- 1985

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 d… Expand

13 lectures on Fermat's last theorem

- Mathematics
- 1979

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 Other… Expand