For the theorem that states that in quadratic field Q[sqrt d], if d is congruent to 1 mod 4, then it is in the form (a + b sqrt d)/2 and if it's not, it's in the form a + b sqrt d where a and b are rational integers, is it saying that if a and b are rational integers and the quadratic number are in the form according to its congruency mod 4, then the quadratic number is an integer?(adsbygoogle = window.adsbygoogle || []).push({});

Also, how would you prove that if 32 = ab where a and b are relatively prime quadratic integers in Q[sqrt -1], a = e(g^2) where e is a unit and g is a quadratic integer in Q [sqrt -1].

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# Quadratic integers help

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