Since Fermat characterized (without proof) those integers represented by the quadratic form x^2+y^2, number theorists have been extending these results.  Recently a paper appeared in Journal of Number Theory answering the question for x^2 ± xy ± y^2.  It turns out that this was not news (although JNT refuses to correct or retract).  Naively, today's speaker extended these results, through elementary means.  This talk will outline these methods, and contrast them with more traditional techniques.