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# Discriminant

The discriminant ${\displaystyle d}$ 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 ${\displaystyle d=2}$, then all numbers in ${\displaystyle \mathbb {Z} [{\sqrt {d}}]}$ are of the form ${\displaystyle a+b{\sqrt {2}}}$, where ${\displaystyle a}$ and ${\displaystyle b\in \mathbb {Z} }$.