Prove that $F = \{\,a^i b^j\mid i = kj \text{ for some positive integer }k\ \}$ is not context free This question is borrowed from sipser 2nd ed.
Show that  $F = \{\,a^i b^j\mid i = kj \text{ for some positive integer }k\ \}$ is not context free.
I tried it but did not get any clue about the scenario ; which shall oppose it being context free.
Let pumping length is  $p$ and suppose we take string $a^{2p} b^p$ for pumping lemma test.
If we take $a^p$ as pumping portion then it'll always be in the language.
$a^i b^j$ | $i = kj$
Please provide me the scenario which shall work out.
Help appreciated :)

Hint: Try to pump $a^{p+1}b^{p+1}$
