Let $K$ be a number field of degree $n$ over the rationals. Under what conditions does there exist an algebraic integer $\alpha $ in $K$ such that the discriminant of $\alpha$ divides the norm of $\alpha$?
2026-04-13 12:34:09.1776083649
Does there always exist an algebraic integer in a number field whose discriminant divides its norm?
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I crossed-posted this question on MathOverflow as it was unanswered after two weeks and held a bounty. The question was then answered there.