I’ve being looking at finding integral bases and particularly at question 6 on the third homework sheet. I’m looking for a integral basis for $Q(\sqrt{2} + \sqrt{3})$ I understand that $(\sqrt{2} + \sqrt{3})/2$ will replace in to form an integral basis but I don’t understand how to get to it. It seems too long winded to try every possible value for $\sum ab/2$ until I find one which is a algebraic integer. What am I missing?
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