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n
≡
2
(
mod.
4
)
{\displaystyle n\equiv 2\quad ({\mbox{mod.}}\,4)}
x
1
=
0
{\displaystyle x_{1}=0}
,
n
2
−
5
{\displaystyle {\tfrac {n}{2}}-5}
x
3
=
7
{\displaystyle x_{3}=7}
,
0
x
4
=
n
2
−
5
{\displaystyle x_{4}={\tfrac {n}{2}}-5}
,
0
x
n
+
2
4
=
0
,
{\displaystyle x_{\frac {n+2}{4}}=0,}
7
x
3
(
n
−
2
)
4
=
0
,
{\displaystyle x_{\frac {3(n-2)}{4}}=0,}
1
x
n
−
4
=
1
{\displaystyle x_{n-4}=1}
,
0
x
1
=
1
{\displaystyle x_{1}=1}
,
n
2
−
3
{\displaystyle {\tfrac {n}{2}}-3}
x
2
=
3
{\displaystyle x_{2}=3}
,
0
x
3
=
2
{\displaystyle x_{3}=2}
,
0
x
4
=
n
2
−
3
{\displaystyle x_{4}={\tfrac {n}{2}}-3}
,
0
x
n
−
2
4
=
0
,
{\displaystyle x_{\frac {n-2}{4}}=0,}
1
x
n
+
2
4
=
0
,
{\displaystyle x_{\frac {n+2}{4}}=0,}
3
x
n
−
2
2
=
0
,
{\displaystyle x_{\frac {n-2}{2}}=0,}
1
x
n
2
=
0
,
{\displaystyle x_{\frac {n}{2}}=0,}
2
x
n
−
4
=
1
,
{\displaystyle x_{n-4}=1,}
0
x
1
=
3
{\displaystyle x_{1}=3}
,
n
2
−
2
{\displaystyle {\tfrac {n}{2}}-2}
x
2
=
3
{\displaystyle x_{2}=3}
,
0
x
4
=
n
2
−
2
{\displaystyle x_{4}={\tfrac {n}{2}}-2}
,
0
x
n
−
2
4
=
0
,
{\displaystyle x_{\frac {n-2}{4}}=0,}
3
x
n
+
2
4
=
0
,
{\displaystyle x_{\frac {n+2}{4}}=0,}
1
x
n
−
4
=
1
{\displaystyle x_{n-4}=1}
,
0
x
1
=
4
{\displaystyle x_{1}=4}
,
n
2
−
3
{\displaystyle {\tfrac {n}{2}}-3}
x
3
=
3
{\displaystyle x_{3}=3}
,
0
x
4
=
n
2
−
3
{\displaystyle x_{4}={\tfrac {n}{2}}-3}
,
0
x
n
−
2
4
=
0
,
{\displaystyle x_{\frac {n-2}{4}}=0,}
3
x
n
+
2
4
=
0
,
{\displaystyle x_{\frac {n+2}{4}}=0,}
4
x
3
n
−
2
4
=
0
,
{\displaystyle x_{\frac {3n-2}{4}}=0,}
1
x
n
−
4
=
1
{\displaystyle x_{n-4}=1}
,
0
n
≡
3
(
mod.
4
)
{\displaystyle n\equiv 3\quad ({\mbox{mod.}}\,4)}
x
1
=
0
{\displaystyle x_{1}=0}
,
n
−
7
2
{\displaystyle {\tfrac {n-7}{2}}}
x
2
=
3
{\displaystyle x_{2}=3}
,
0
x
3
=
3
{\displaystyle x_{3}=3}
,
0
x
4
=
n
−
7
2
{\displaystyle x_{4}={\tfrac {n-7}{2}}}
,
0
x
n
+
1
4
=
0
,
{\displaystyle x_{\frac {n+1}{4}}=0,}
3
x
n
+
5
4
=
0
,
{\displaystyle x_{\frac {n+5}{4}}=0,}
1
x
n
−
1
2
=
0
,
{\displaystyle x_{\frac {n-1}{2}}=0,}
3
x
n
−
4
=
1
{\displaystyle x_{n-4}=1}
,
0
x
1
=
1
{\displaystyle x_{1}=1}
,
n
−
9
2
{\displaystyle {\tfrac {n-9}{2}}}
x
3
=
6
{\displaystyle x_{3}=6}
,
0
x
4
=
n
−
9
2
{\displaystyle x_{4}={\tfrac {n-9}{2}}}
,
0
x
n
+
1
4
=
0
,
{\displaystyle x_{\frac {n+1}{4}}=0,}
6
x
n
+
5
4
=
0
,
{\displaystyle x_{\frac {n+5}{4}}=0,}
1
x
3
n
−
5
4
=
0
,
{\displaystyle x_{\frac {3n-5}{4}}=0,}
1
x
n
−
4
=
1
{\displaystyle x_{n-4}=1}
,
0
x
1
=
2
{\displaystyle x_{1}=2}
,
n
−
5
2
{\displaystyle {\tfrac {n-5}{2}}}
x
2
=
3
{\displaystyle x_{2}=3}
,
0
x
3
=
1
{\displaystyle x_{3}=1}
,
0
x
4
=
n
−
5
2
{\displaystyle x_{4}={\tfrac {n-5}{2}}}
,
0
x
n
−
3
4
=
0
,
{\displaystyle x_{\frac {n-3}{4}}=0,}
1
x
n
+
1
4
=
0
,
{\displaystyle x_{\frac {n+1}{4}}=0,}
3
x
n
−
1
2
=
0
,
{\displaystyle x_{\frac {n-1}{2}}=0,}
2
x
n
+
1
2
=
0
,
{\displaystyle x_{\frac {n+1}{2}}=0,}
1
x
n
−
4
=
1
{\displaystyle x_{n-4}=1}
,
0
x
1
=
5
{\displaystyle x_{1}=5}
,
n
−
5
2
{\displaystyle {\tfrac {n-5}{2}}}
x
3
=
2
{\displaystyle x_{3}=2}
,
0
x
4
=
n
−
5
2
{\displaystyle x_{4}={\tfrac {n-5}{2}}}
,
0
x
n
−
3
4
=
0
,
{\displaystyle x_{\frac {n-3}{4}}=0,}
2
x
n
+
1
4
=
0
,
{\displaystyle x_{\frac {n+1}{4}}=0,}
5
x
3
n
−
1
4
=
0
,
{\displaystyle x_{\frac {3n-1}{4}}=0,}
1
x
n
−
4
=
1
{\displaystyle x_{n-4}=1}
,
0