Solutions and Remarks for Homework                  Section 1.5, page 37
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#18.  alpha^m = 1  =>  alpha = exp(2k\pi/m), k=0, 1, ..., m-1.
      beta^n = 1  =>  beta = exp(2t\pi/n), t=0,1,...,n-1.

      Thus, alpha.beta = exp[2(nk+mt)\pi/mn]=exp[2r\pi/mn], where
      r=nk+mt. Hence, since r is an integer alpha.beta is a mn-th
      root of unity.