# Is there a way to have FindInstance or Solve give only positive integer solutions?

I keep getting either negative or super long answers or super long negative answers in no particular order :\ ... Is there a way to only ask for positive solutions? (here we want 0 < x<(10^12+y) I tried using Assumptions but it didn't work :<

FindInstance[ 1/2 == x/(1000000000000 + y)*(x - 1)/(1000000000000 + y - 1), {x,  y}, Integers]


FindInstance[