5
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Well, here's my question:

Are there any integers, $a$ and $b$ that satisfy the equation $b^2$$+4$=$a^3$, such that $a$ and $b$ are coprime?

I've already found the case where $b=11$ and $a =5$, but other than that? And if there do exist other cases, how would I find them? And if not how would I prove so?

Thanks in advance. :)

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    Well, then you should also remove the part asking for the proof of their non-existence-if-they-don't in your edit. Tricky among other things.2012-12-22
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    Oh, yikes. I'm sorry. You're right. It was misleading. I think it's okay now, though.2012-12-22

4 Answers 4