<http://www.eurekalert.org/pub_releases/2009-09/aiom-att091809.php>
Mathematicians from North America, Europe, Australia, and South America have resolved the first one trillion cases of an ancient mathematics problem. ...
The problem, which was first posed more than a thousand years ago, concerns the areas of right-angled triangles. The surprisingly difficult problem is to determine which whole numbers can be the area of a right- angled triangle whose sides are whole numbers or fractions. ...
/Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
That article doesn't motivate the gigantic integers. It should have given Zagier's 157 exemplar: If a:=6803298487826435051217540/411340519227716149383203, b:=411340519227716149383203/21666555693714761309610, c:=224403517704336969924557513090674863160948472041 /8912332268928859588025535178967163570016480830 then a^2+b^2 = c^2, and ab/2 = 157 . It would be nice to know the (logarithms of the) grossest one they found. Also not crystal clear: Does the validity of the computation hinge on Birch&Swinnerton-Dyer? Would finding a conger not in their list refute B&S-D? --rwg