Math help

First, since x and y are integers so are xy and x+ y so x and y must be such that \(\displaystyle \sqrt{x^2+ y^2}\) is an integer- think "Pythagorean triples".
 
This is what I ve tried so far , I think I need to factorize it further , but I ve no idea how to factorize , if at all this is the correct way of starting off

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You can, of course, factor out xy. Then if you try to factor by grouping, you will find that it comes close, resulting in something of the form (...)(...)-... = 0

That leads to something you can do using the fact that x and y must be integers ...
 
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You can, of course, factor out xy. Then if you try to factor by grouping, you will find that it comes close, resulting in something of the form (...)(...)-... = 0


That leads to something you can do using the fact that x and y must be integers ...

Well I factorized it out , and I got just 1 pair of integers as x=16 and y = 30 . I got just this one pair . Is it right ?
 
Well I factorized it out , and I got just 1 pair of integers as x=16 and y = 30 . I got just this one pair . Is it right ?

No, I found more pairs than that (and even your answer would yield two different ordered pairs). Can you show your details?
 
Ok now I tried it again and found 3*2=6 pairs (14,48);(16,30);(18,24) and vice versa
Is it correct now ?
 

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No, there are still more. I don't think you've shown all your work, as there is no indication where you are getting your numbers from, and I don't see anything factored. what are you "trying 2, 4, 5, 6" in?
 
Check your arithmetic! All those pairs work; there's no reason they shouldn't, given the factoring.

(Before I replied to you in the first place, I put them all into a spreadsheet to make sure they worked.)

(By the way, your notation "= Z" is poor notation; Z is a set, and a number can't equal a set.)
 
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