Context-free string that satisfies constraint? I'm not sure on how to come up with a string that is in terms of $p$ for

$ a^ib^jc^k$  where $ i+j = k^2$

Where $p$ is the pumping length. I can't seem to find anything in terms of $p$ that satisifies the constraint. Any ideas or sugeestions are appreciated!
It is not necessary to define a string that has exactly length $p$. It only has to have length at least $p$. So $(i,j,k) = (2p^2,2p^2,2p)$ so that $2p^2+2p^2 = (2p)^2$ for a string of length $4p^2+2p$ would be OK.