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If \(x+y\)\(x^2+y^2\)\(x^3+y^3\), and \(x^4+y^4\) are all integers, and \(x\) and \(y \) are both real numbers, do \(x\) and \(y\) have to be integers as well?

 Feb 20, 2022
 #1
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I think so. 

Here is my reasoning: \(x^2+y^2= (x+y)^2-2xy\), since we know x+y is an integer, and x^2+y^2 is also an integer, then -2xy must be an integer. 

 

maybe someone else can do this as well?

 Feb 20, 2022
 #2
avatar+226 
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yes, but just because 2xy is an integer, it doesn't say anything about x, y, or xy.

thats where im stumped

 Feb 20, 2022
 #3
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I have played with this for ages but I have not come up with anything helpful :((

 Feb 21, 2022

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