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Let d be an integer. Prove that is an integral domain.

Chapter 13, Problem 11E

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QUESTION:

Let d be an integer. Prove that \(Z[\sqrt d] = \{a + b \sqrt d | a, b \in Z\}\) is an integral domain. (This exercise is referred to in Chapter 18.)

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QUESTION:

Let d be an integer. Prove that \(Z[\sqrt d] = \{a + b \sqrt d | a, b \in Z\}\) is an integral domain. (This exercise is referred to in Chapter 18.)

ANSWER:

Step 1 of 7

Let d be an integer. To prove is an integral domain, argue as follows.

Consider two cases

        

        

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