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Possible Duplicate:
Methods for quartic diophantine equation

Find all solutions of the Diophantine Equation 3x^2 + 2y^4 = z^4

I have just found x=0, y=o, and z=0. I think that I need to use some congruence theory here, but I'm not really sure. I was suggested that if I tried the assumption that either y or z are divisible by three I would get a contradiction, but I have worked on it, and I can't really see it.

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    I just asked about [this exact same equation](http://math.stackexchange.com/questions/134987/methods-for-quartic-diophantine-equation)... where did you come across it?2012-04-25
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    It's homework. I read your question, and that's exactly what I need to know: how do you decide to use congruence mod3? I already have a solution,but I just don't understand it.2012-04-25
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    Well there *is* a $3$ in the equation, but I feel your pain. I tried to get a motivation for that selection of modulus, to no avail...2012-04-25
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    Sorry, Nathan, you're not making sense. In the question you say you don't have a solution, in the comment you say you do. Why don't you rethink your question, lay all your cards on the table, and ask us what you really want to ask.2012-04-25
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    @TheChaz, I give what amounts to a procedure at your related question, with a link to a key ingredient at another of my answers.2012-04-25
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    @WillJagy: I saw that, and have symbolically indicated my gratitude with an upvote. I'll have to think about it after some sleep. Thanks (again?)!2012-04-25

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