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Due October 25. Let Z[i] denote the Gaussian integers, with norm N(a + bi) = a...

Due October 25. Let Z[i] denote the Gaussian integers, with norm N(a + bi) = a 2 + b 2 . Recall that ±1, ±i are the only units i Z[i]. (i) Use the norm N to show that 1 + i is irreducible in Z[i]. (ii) Write 2 as a product of distinct irreducible elements in Z[i].

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