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Let $p \ge 7$ be a prime number. Find the triples $(x, y, z)$ in $\mathbb{Z}$ such as $xyz$ is not equal to zero, $\gcd (x, y, z) = 1$ and $x^p + 2y^p = z^2$. I want triplets and proof/generalization. The reason for asking here, I am in position to construct equations and finding solutions by trail method. I am not in position to construct a proof or good generalizations. I hope, with your help, I can end.

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    Anyone who is a Number Theory guru here, please let me know if someone posts an open problem, how is it handled here (Any guidelines??)2012-03-24
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    I think questions about the working of the site itself are best answered at [meta] best! @KVRaman2012-03-24
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    @KVRaman Except for the "best" at the end, which was redundant, I have conveyed what I wanted to convey to the best of my ability. If you do not understand, it is better ignored. You may not understand it any later.2012-03-24
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    @KannappanSampath I do get it now. You mean about the guidelines I can find answer on meta.math.se (Of course!) Thanks2012-03-24
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    Just added tag "open-problem" because someone(on meta math) posted an answer to my question about this tag.2012-03-27
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    @KannappanSampath Thanks for Mathematics Meta (I got an answer from someone that there is an open-problem tag)2012-03-27

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