a2+b2=c2 and ab/2=2014

     Happy New Year!

     Cool!!! 2014 is a congruent number!


     
     Substitute n=2014 to y2=x3-n2x and solve about (x,y), then we obtain
     (x,y)=(131323478/85849,1288816101144/25153757)

     a=(n2-x2)/y=18244332/544687

     b=2nx/y=28868411/240057

     c=(n2+x2)/y=16322793093085/130755927159

     a2+b2=c2 and ab/2=2014