# Three Fermat Trails to Elliptic Curves

@article{Brown2000ThreeFT,
title={Three Fermat Trails to Elliptic Curves},
author={Ezra Brown},
journal={The College Mathematics Journal},
year={2000},
volume={31},
pages={162 - 172}
}
• Ezra Brown
• Published 2000
• Mathematics
• The College Mathematics Journal
Ezra (Bud) Brown (brown@math.vt.edu) professes mathematics at Virginia Tech, where he has been since 1969. The elliptic curve bug first bit him while he was in graduate school at Louisiana State, and has never really gone away. Although his main research has been in quadratic forms and algebraic number theory, he once wrote a paper with a sociologist. He loves to talk about mathematics and its history with anyone, especially students. He occasionally sings in operas, plays jazz piano just for… Expand
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#### References

SHOWING 1-10 OF 29 REFERENCES
Factoring integers with elliptic curves
This paper is devoted to the description and analysis of a new algorithm to factor positive integers that depends on the use of elliptic curves and it is conjectured that the algorithm determines a non-trivial divisor of a composite number n in expected time at most K( p)(log n)2. Expand
Introduction to Elliptic Curves and Modular Forms
The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This bookExpand
Rational Points on Elliptic Curves
• Mathematics
• 1992
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing anExpand
Introduction to Fermat's Last Theorem
The announcement last summer of a proof of Fermat's Last Theorem was an exciting event for the entire mathematics community. This article will discuss the mathematical history of Fermat's LastExpand
Elliptic Curves
These are the notes for Math 679, University of Michigan, Winter 1996, exactly as they were handed out during the course except for some minor corrections. Please send comments and corrections to meExpand
Elliptic curve cryptosystems
We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure,Expand
Ring-Theoretic Properties of Certain Hecke Algebras
• Mathematics
• 1995
The purpose of this article is to provide a key ingredient of [W2] by establishing that certain minimal Hecke algebras considered there are complete intersections. As is recorded in [W2], a methodExpand
Use of Elliptic Curves in Cryptography
• V. Miller
• Mathematics, Computer Science
• CRYPTO
• 1985
An analogue of the Diffie-Hellmann key exchange protocol is proposed which appears to be immune from attacks of the style of Western, Miller, and Adleman. Expand
Mathematics and its history
Preface.- The Theorem of Pythagoras.- Greek Geometry.- Greek Number Theory.- Infinity in Greek Mathematics.- Polynomial Equations.- Analytic Geometry.- Projective Geometry.- Calculus.- InfiniteExpand
Almost all primes can be quickly certified
• Mathematics, Computer Science
• STOC '86
• 1986
A new probabilistie primality test is presented, different from the tests of Miller, Solovay-Strassen, and Rabin in that its assertions of primality are certain, rather than being correct with high probability or dependent on an unproven assumption. Expand