This is actually a Number Theory question, but requires expertise that doesn't go beyond simple algebra.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Show that (1+xy)(1+zy)(1+zx) is a perfect square iff (1 + xy), (1+yz) , and (1+zx) are perfect squares.

2. Relevant equations

3. The attempt at a solution

I initially tried to solve it like this

let 1 + xy = s^{2}, 1 + yz = t^{2}, 1 + zx = u^{2}. I substituted the new variables and got

(1+xy)(1+zy)(1+zx) = s^{2}t^{2}u^{2}- s^{2}t^{2}+t^{4}-t^{2}+s^{2}

I tried to get the RHS of the equation to be in some square form, but couldn't. I thought that introducing new variables to the problem would add to the complexity of the problem, but I thought that adding new variables would give me a new way to solve the problem also.

So .. any thoughts?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Algebraic Number Theory Question

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