Let w D a C b p 3 2 Z p 3. Define the norm of w to be N.w/ D a 2 C 3b2 : Please do the
Chapter 39, Problem 39.25(choose chapter or problem)
Let w D a C b p 3 2 Z p 3. Define the norm of w to be N.w/ D a 2 C 3b2 : Please do the following: a. Prove that if w; z 2 Z p 3, then N.wz/ D N.w/N.z/. b. Find all w 2 Z p 3 with N.w/ D 0, with N.w/ D 1, with N.w/ D 2, with N.w/ D 3, and with N.w/ D 4.
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