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A new criterion for congruent primes
by
Nils Bruin
Simon Fraser University
Coauthors: Brett Hemenway
An integer is called congruent if it is the area of a right triangle with rational sides.
It is an old result that testing whether a number is congruent amounts to deciding if a
certain elliptic curve is of positive rank.
Tunnell's theorem solved the congruent number problem almost completely, but questions remain.
Some insight can be obtained from looking at some earlier elementary criteria for congruent primes and trying to extend those methods.
This leads to interesting problems. I will discuss some of these problems and show what new questions arise.
Date received: June 6, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawl-68.