Show transcribed image text Problem D. Let's try to figure out how to define "phi(d) for a Gaussian integer d. Suppose S is a set of Gaussian integers such that every n in Z[] can be written uniquely as qd+r, with q n Z i and r in S So for instance when d=1 +2 we showed in problem B that we can take S to be o. 4 it would a sobe o a s i e 5 r 10,i,2i,1+i,1+2i). In fact, it turns out that S has to be a set of size Norm(d) (I might or might not prove this in class; if not, feel free just to accept it.) Now define phi(d) to be the number of elements s of S such that s and d are coprime.
Problem D. Let's try to figure out how to define "phi(d) for a Gaussian integer d. Suppose S is a set of Gaussian integers such that every n in Z[] can be written uniquely as qd+r, with q n Z i and r in S So for instance when d=1 +2 we showed in problem B that we can take S to be o. 4 it would a sobe o a s i e 5 r 10,i,2i,1+i,1+2i). In fact, it turns out that S has to be a set of size Norm(d) (I might or might not prove this in class; if not, feel free just to accept it.) Now define phi(d) to be the number of elements s of S such that s and d are coprime.
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