: 3.° le quattro curve ${\displaystyle a^{{\tfrac {n}{3}}-1}t_{1}t_{2}\dots t_{{\tfrac {2n}{3}}-2}d(o_{1},o_{2},o_{3},o_{4})}$ d’ordine ${\displaystyle {\tfrac {n}{3}}}$; e

4.° la curva ${\displaystyle a^{{\tfrac {2n}{3}}-2}t_{1}^{2}t_{2}^{2}\dots t_{{\tfrac {2n}{3}}-2}^{2}do_{1}o_{2}o_{3}o_{4}}$ d’ordine ${\displaystyle {\tfrac {2n}{3}}}$.

Per tal modo, nel caso che ${\displaystyle n}$ sia un multiplo di ${\displaystyle 3}$, otteniamo le due coppie seguenti di soluzioni coniugate delle equazioni (1), (2):

${\displaystyle n}$ multiplo di 3 ${\displaystyle x_{1}=1,\,{\frac {2n}{3}}-3}$ ${\displaystyle x_{1}=4,\,{\frac {2n}{3}}-2}$ ${\displaystyle x_{2}=4,\,0}$ ${\displaystyle x_{2}=1,\,0}$ ${\displaystyle x_{3}={\frac {2n}{3}}-3,\,0}$ ${\displaystyle x_{3}={\frac {2n}{3}}-2,\,0}$ ${\displaystyle x_{4}=0,\,4}$ ${\displaystyle x_{{\tfrac {n}{3}}-1}=0,\,1}$ ${\displaystyle x_{{\tfrac {n}{3}}+1}=0,\,1}$ ${\displaystyle x_{\tfrac {n}{3}}=0,\,4}$ ${\displaystyle x_{{\tfrac {2n}{3}}-1}=0,\,1}$ ${\displaystyle x_{\tfrac {2n}{3}}=0,\,1}$ ${\displaystyle x_{n-3}=1,\,0}$ ${\displaystyle x_{n-3}=1,\,0}$

Analogamente, considerando i casi che il numero ${\displaystyle n}$ sia della forma ${\displaystyle 3\mu +1}$ o della forma ${\displaystyle 3\mu +2}$, si hanno le coppie di soluzioni coniugate che seguono:

${\displaystyle n\equiv 1}$ (mod. 3) ${\displaystyle x_{1}=2,\,{\frac {2n-8}{3}}}$ ${\displaystyle x_{1}=5,\,{\frac {2n-5}{3}}}$ ${\displaystyle x_{2}=3,\,0}$ ${\displaystyle x_{3}={\frac {2n-8}{3}},\,0}$ ${\displaystyle x_{3}={\frac {2n-5}{3}},\,0}$ ${\displaystyle x_{\tfrac {n-1}{3}}=0,\,3}$ ${\displaystyle x_{\tfrac {n-1}{3}}=0,\,5}$ ${\displaystyle x_{\tfrac {n+2}{3}}=0,\,2}$ ${\displaystyle x_{\tfrac {2n+1}{3}}=0,\,1}$ ${\displaystyle x_{\tfrac {2(n-1)}{3}}=0,\,1}$ ${\displaystyle x_{n-3}=1,\,0}$ ${\displaystyle x_{n-3}=1,\,0}$