[[Hint: Let be sides of a rational right triangle with area . Let .]]
and
given explicitly by the maps
and
http://www.msri.org/publications/ln/msri/2000/introant/ yui/1/index.htmland read about another difficult generalization of the congruent number problem (this was a talk at a serious professional research conference, so don't be annoyed if you don't understand much of it).
William Stein 2006-07-07