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2002 Taiwan National Olympiad
1
1
Part of
2002 Taiwan National Olympiad
Problems
(1)
find n and n nonnegative integers
Source: 11-th Taiwanese Mathematical Olympiad 2002
1/22/2007
Find all natural numbers
n
n
n
and nonnegative integers
x
1
,
x
2
,
.
.
.
,
x
n
x_{1},x_{2},...,x_{n}
x
1
,
x
2
,
...
,
x
n
such that
∑
i
=
1
n
x
i
2
=
1
+
4
4
n
+
1
(
∑
i
=
1
n
x
i
)
2
\sum_{i=1}^{n}x_{i}^{2}=1+\frac{4}{4n+1}(\sum_{i=1}^{n}x_{i})^{2}
∑
i
=
1
n
x
i
2
=
1
+
4
n
+
1
4
(
∑
i
=
1
n
x
i
)
2
.
number theory proposed
number theory