I have to prove:

(a^i) (b^j) (a^(i.j) ) | i, j > =0; non regular using pumpimg Lemma. I have to suppose a string.

Let w = (a^m) . (b^m) . (a^(m.m))

I have to find xy in this string such that |xy| >= m

(a^m) = |xy|

(b^m) = |xy|

(a^(m.m)) = |xy| + |xy|

Now xyz = (a^m) ...Problem?

What would be 'z' here? Some body please guide me.

Zulfi.