**Sipser Exercise 1.53**

Let and

This language is not regular.

*Proof*:
Suppose were regular and let be the pumping length.
Take to be the string , noting that and .
Then let such that and .

We see that and consist entirely of ’s, that is, for some . But is . Looking at the right-hand side, the sum must have in the ‘th spot, so this equation cannot be correct, and this string is not in , contradicting the pumping lemma. So is not regular.