Question from Sipser, exercise 2.29.
Prove that the language $A = \{a^ib^jc^k | i = j \text{ or } j = k \}$ is inherently ambiguous, that is, every grammar which generates $A$ is ambiguous.
So the problem here appears to be the case when $i = j = k$. The language should be able to generate strings of the form $a^ib^jc^j$, where the number of $a$'s during the generation is "independent" in some sense of the number of $b$'s and $c$'s. A similar phenomenon "should" occur with strings of the form $a^ib^ic^j$. Then, if you are dealing with a string of the form $a^ib^ic^i$, it "shouldn't be able" to tell if it came from the first algorithm where $a's$ are immaterial or the second algorithm where $c$'s are immaterial.
However, given the number of scare quotes I've placed in the above paragraph, it's probably clear that I'm out to lunch on how to prove this.