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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?

 Nov 16, 2018
 #1
avatar+6026 
+2

I'm showing 2305

 

What class is this?  Is there supposed to be some clever way of figuring this out?

 Nov 17, 2018
 #2
avatar+700 
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I am pretty sure this is number theory. 

 Nov 19, 2018
 #3
avatar+700 
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I think Vieta's formula might work in here, but I am not sure how to proceed.

 Nov 19, 2018

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