Let R = ℤ/3ℤ, the integers mod 3. The ring of Gaussian integers mod 3 is defined by R[i] = { a + bi : a, b ∈ ℤ/3ℤ and ? = √−1 }. Show that R[i] is a field.

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Q: Let R= Z/3Z, the integers mod 3. The ring of Gaussian integers mod 3 is defined by R[i] = {a+ bi :…

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Q: Let R = Z/3Z, the integers mod 3. The ring of Gaussian integers mod 3 is defined by R[i] = { a + bi…

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Q: C. Prove that neither 2 nor 17 are prime elements in Z[i] (the ring of Gaussian integers).

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