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Spain Mathematical Olympiad
1999 Spain Mathematical Olympiad
2
2
Part of
1999 Spain Mathematical Olympiad
Problems
(1)
a_1^2+a_2^2+...+a_n^2 a perfect square
Source: 1999 Spanish Mathematical Olympiad P2
7/21/2018
Prove that there exists a sequence of positive integers
a
1
,
a
2
,
a
3
,
.
.
.
a_1,a_2,a_3, ...
a
1
,
a
2
,
a
3
,
...
such that
a
1
2
+
a
2
2
+
.
.
.
+
a
n
2
a_1^2+a_2^2+...+a_n^2
a
1
2
+
a
2
2
+
...
+
a
n
2
is a perfect square for all positive integers
n
n
n
.
number theory
Perfect Square
Integer sequence