Definition:Apotome/First Apotome

Definition
Let $a, b \in \R_{>0}$ be (strictly) positive real numbers such that $a - b$ is an apotome.

Then $a - b$ is a first apotome iff $a \in \Q$ and $\dfrac {\sqrt {a^2 - b^2}} a \in \Q$, where $\Q$ denotes the set of all rational numbers.



Example
When $a = 9$ and $b = \sqrt {17}$,

Therefore $9 - \sqrt {17}$ is a first apotome.