There are 4 positive integers: a, b, c, d
With the following conditions:
1 < a < b < c < d < 1000
b+c = a+d
bc - ad = 2004
How many sets of (a, b, c, d) are there?
I'm showing 2305
What class is this? Is there supposed to be some clever way of figuring this out?
I think Vieta's formula might work in here, but I am not sure how to proceed.