I have question where it asks:
Using the pumping lemma on a^N b^N a^2N, why can you not reach a contradiction when k=2?
Here's what I've done, but I do reach a contradiction...
u=a^r v=a^s x=a^t b^N a^2N
When k=2, then uv^2x=a^N+s b^N a^2N
Therefore, this is a contradiction as N+s>N.
Is this a contradiction?