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  3. for any gaussian integer z ? ?[i] with z = a+bi ,

For any Gaussian Integer z ? ?[i] with z = a+bi , define N(z) =a2 +...

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Advance Math

For any Gaussian Integer z ? ?[i] with z = a+bi , define N(z)=a2 + b2. Using the division algorithm forthe Gaussian Integers, we have show that there is at least one pairof Gaussian integers q and r such that w = qz + r with N(r)

(a) Assuming z does not divide w, show that there are always twosuch pairs.

(b) Fine Gaussian integers z and w such that there are fourpairs of q and r that satisfy the division algorithm with N(r)

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