The key to this particular problem is making sure all of the elements are of the form a + b5 Let (a + b5) & (c+ d5) € A Consider bd(¥5)² (a + b5) · (c+ dW5) = ac + ad5 + bcỷ5+i Note bd(5) ¢ A. This is not closed over multipliciation and therefore not a ring. Can you explain why bd(5) £ A?

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