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?