Proving the regularity of the following language I have a question about the following problem:


  Prove that the language $\{a^nva^n | v \in \Sigma^*, n \ge 1\}$ is regular over
  $\Sigma = \{a,b\}.$


I know that in proving a language is regular I can either construct a DFA, give a regular expression or show the Nerode-Relation has finite index.

My main problem is, that I cannot understand why this should be a regular language, since $\{a^nb^n | n \ge 1\}$ is not regular and of similar form. Also, I do not understand how a DFA should recognize the same amount of a's at the front and at the end of a word.
You can always take $n = 1$ for any string in your language...