Unter der
β
{\displaystyle {}\beta }
Funktion
versteht man die Abbildung
N
3
⟶
N
,
(
p
,
n
,
i
)
⟼
β
(
p
,
n
,
i
)
,
{\displaystyle \mathbb {N} ^{3}\longrightarrow \mathbb {N} ,\,(p,n,i)\longmapsto \beta (p,n,i),}
die folgendermaßen festgelegt ist.
β
(
p
,
n
,
i
)
{\displaystyle {}\beta (p,n,i)}
a
∈
N
{\displaystyle {}a\in \mathbb {N} }
b
0
,
b
1
,
b
2
{\displaystyle {}b_{0},b_{1},b_{2}}
n
=
b
0
+
b
1
(
(
i
+
1
)
+
a
p
+
b
2
p
2
)
{\displaystyle {}n=b_{0}+b_{1}{\left((i+1)+ap+b_{2}p^{2}\right)}}
a
<
p
{\displaystyle {}a<p}
b
0
<
b
1
{\displaystyle {}b_{0}<b_{1}}
b
1
{\displaystyle {}b_{1}}
Alle Teiler
d
≠
1
{\displaystyle {}d\neq 1}
b
1
{\displaystyle {}b_{1}}
p
{\displaystyle {}p}
Wenn kein solches
a
{\displaystyle {}a}
β
(
p
,
n
,
i
)
=
0
{\displaystyle {}\beta (p,n,i)=0}
