FIND OUT ALL POSITIVE INTEGER SOLUTIONS
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Find all the positive integer solution of the equation 3(xy+yz+zx)=4xyz.
- Nadim Ul Abrar
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Re: FIND OUT ALL POSITIVE INTEGER SOLUTIONS
In these kind of equations, one of my usual tactics is to convert them in divisibility relations since they are easy to deal with. Re-write as \[3x(y+z)+3yz=4xyz\]MATHPRITOM wrote:Find all the positive integer solution of the equation 3(xy+yz+zx)=4xyz.
Or \[x(4yz-3y-3z)=3yz\]
This forces $y,z$ to be such that \[4yz-3y-3z|3yz\Rightarrow 4yz-3y-3z\le3yz\Rightarrow yz\le3(y+z)\Rightarrow y(z-3)\le3z\]
Now we can find $y,z$ very easily.
One one thing is neutral in the universe, that is $0$.