Michael Sipser Edition 3 Exercise 2 Question 33 (Page No. 157)

Question

Show that $F = \{a^{i}b^{j}\mid i = kj$ $\text{for some positive integer $k$\}}$ is not context free$.$

Answer 1

but, the given expression is context-free where we can prove it by using PDA in which we push every kth a onto the stack and will pop a for every b. thus, proving it to be context-free.