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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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    @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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