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  1. a) Find the characteristic roots of the linear homogeneous recurrence relation $a_{n} = a_{n-4}.$ [Note: These include complex numbers.]
  2. Find the solution of the recurrence relation in part $(A)$ with $a_{0} = 1, a_{1} = 0, a_{2} = -1,\: \text{and}\: a_{3} = 1.$
     

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