1. (10 points). ={a,b}, L = { s : s =a^mb^n, n > 0, m % n = 0 }. (You can also think of this as n divides m evenly, or that m/n is an integer). Use the regular language pumping theorem to prove that L is not a regular language. Hint: choose w with extra care, and then be careful when you argue that w', generated by pumping w, is excluded by L's characteristic function. If your proof runs into problems that you cannot resolve, explain.