${\displaystyle {}a,b\in \mathbb {N} }$

${\displaystyle {}ab\leq a^{2}+b^{2}\,}$

gilt und somit stets ${\displaystyle {}a^{2}+b^{2}-ab\in \mathbb {N} }$ ist.

${\displaystyle \mathbb {N} \times \mathbb {N} \longrightarrow \mathbb {N} ,\,(a,b)\longmapsto a\star b:=a^{2}+b^{2}-ab,}$

ein neutrales Element?

${\displaystyle 5\star (4\star 3).}$