The Oldest Unsolved Problem in Mathematics -- Mark Xue, September 20, 2004

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A congruent number is an integer which can be expressed as the area of 
a right triangle with rational sides. The question of characterizing 
all congruent numbers goes back to antiquity, and has motivated some 
beautiful mathematics. I will describe two classical results and 
explain how the congruence problem is related to the arithmetic of 
elliptic curves.