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Brimley
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Hello PhysicsForums!
I had posted a question earlier today in another thread and I had a follow up question to it (the question in nature isn't extremely related, but the link can be found https://www.physicsforums.com/showthread.php?p=2964009#post2964009").
In the previous example, it was listed that [itex]\lambda = (3+\sqrt{-3})/2 \in \mathbb{Q}[\sqrt{3}][/itex].
The text states the following:
"[itex]x,y,[/itex] and [itex]z[/itex] are quadratic integers in [itex]\mathbb{Q}[\sqrt{-3}][/itex], where [itex]x^3 + y^3 = z^3[/itex]." From here it can be shown that [itex]\lambda[/itex] can divide one of [itex]x,y,[/itex] or [itex]z[/itex].
Can anyone help explain this? I don't know if reducing the equation modula [itex]\lambda^3[/itex] would help, but its my first guess.
Thanks -- Brim
I had posted a question earlier today in another thread and I had a follow up question to it (the question in nature isn't extremely related, but the link can be found https://www.physicsforums.com/showthread.php?p=2964009#post2964009").
In the previous example, it was listed that [itex]\lambda = (3+\sqrt{-3})/2 \in \mathbb{Q}[\sqrt{3}][/itex].
The text states the following:
"[itex]x,y,[/itex] and [itex]z[/itex] are quadratic integers in [itex]\mathbb{Q}[\sqrt{-3}][/itex], where [itex]x^3 + y^3 = z^3[/itex]." From here it can be shown that [itex]\lambda[/itex] can divide one of [itex]x,y,[/itex] or [itex]z[/itex].
Can anyone help explain this? I don't know if reducing the equation modula [itex]\lambda^3[/itex] would help, but its my first guess.
Thanks -- Brim
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