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I was initially working with a different problem which I solved very easily. Anyway, the problem I'm going to post now, may not be of any particular interest, but I want to have some help towards solving it.

Suppose that $a$, $b$ are two non-negative integers satisfying: $$a^{2n+1}+b^{2n+1}\text{ is a perfect square for all non-negative integers }n$$ (i.e. $a+b$, $a^3+b^3$, $a^5+b^5$, etc. are all perfect squares). Are there any such $a$ and $b$, such that none of $a$ and $b$ is 0?

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    And we want to exclude $a=b=2$, and relatives.2012-06-13
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    Right, Andre Nicolas and Serkan. Exclude the cases a=b=some odd power of 2, which I missed out. So generally speaking, find all possible such a,b.2012-06-13
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    For what it's worth, I don't think any examples are known of $a^5+b^5=c^2$ for relatively prime $a,b,c$. The standard conjectures would say there are at most finitely many. This doesn't directly apply to the problem at hand, but it shows what you're up against.2012-06-13

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