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Junior Balkan MO
1997 Junior Balkan MO
5
5
Part of
1997 Junior Balkan MO
Problems
(1)
to be even or to be odd,this is the matter :D
Source: JBMO 1997, Problem 5
6/11/2004
Let
n
1
n_1
n
1
,
n
2
n_2
n
2
,
…
\ldots
…
,
n
1998
n_{1998}
n
1998
be positive integers such that
n
1
2
+
n
2
2
+
⋯
+
n
1997
2
=
n
1998
2
.
n_1^2 + n_2^2 + \cdots + n_{1997}^2 = n_{1998}^2.
n
1
2
+
n
2
2
+
⋯
+
n
1997
2
=
n
1998
2
.
Show that at least two of the numbers are even.