Discriminant

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The discriminant $d$ of a quadratic integer ring is a constant that determines the form of the algebraic integers in that ring. It is generally stipulated that a discriminant must be squarefree. For example, if $d=2$, then all numbers in $\mathbb {Z} [{\sqrt {d}}]$ are of the form $a+b{\sqrt {2}}$, where $a$ and $b\in \mathbb {Z}$.