# How do I prove Berman's theorem?

Berman's theorem states

If a unary language ( a language with all the strings of the type $1^i$, $i > 0$ ) is NP-Complete then P = NP.

I tried reducing SAT to a given unary language $L$ assuming it is NP-Complete. But I can't think of a way such that after applying the reduction so that SAT gets solved in polynomial time. How do I proceed further?

This is an exercise from Sanjeev Arora and Boaz Barak , but not homework.