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**Alex2704****Member**- Registered: 2017-01-02
- Posts: 4

Hello! I have recently found a problem and I don't know what this notation means.The problem says : find all the triples (x,y,z) for which

{(x-y)/(y-z),(y-z)/(z-x),(z-x)/(x-y)}={x,y,z}.I don't understand what {x,y,z} means.Thanks in advance!

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

I think it means:

There does not appear to be any solutions in integers and an infinite number in reals.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Alex2704****Member**- Registered: 2017-01-02
- Posts: 4

Oh right.Thanks for your speedy reply !

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

There will need to be some constraints put on x,y and z to have a question.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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If they're integers, you could multiply all the factors on the LHS together to get xyz = 1, then check the different cases.

**LearnMathsFree: Videos on various topics.New: Integration Problem | Adding FractionsPopular: Continued Fractions | Metric Spaces | Duality**

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