Find 4 different positive integers A,B,C,D for which:
A+B = C*D and
A*B = C+D
How many sets of 4 numbers can you find? Prove that only those sets exist.
(In reply to No Subject
I believe your proof has an error somewhere, since as other comments
have mentioned, there is a counterexample to your proof. So I
started to check over all the math.
The point where you lost me was when you started to include the variable x. How is x defined?
Otherwise, the proof seems to make sense until the final
conclusion. It seems that if you solve for A as a function of C
and D, you get two roots (since A and B can switch values). These
two roots are in fact equal to A and B.
I'm still not sure what x is for, but it seems that it must be C or D
(remembering that C and D can switch values). So how do you
conclude from this that two of the variables are equal?
Edited on July 22, 2005, 4:14 am
Posted by Tristan
on 2005-07-22 04:02:59