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2019 All-Russian Olympiad
2
ARMO 2019 9.2
ARMO 2019 9.2
Source: All-Russian Math Olympiad 2019
July 11, 2019
ARMO
Problem Statement
Find minimal natural
n
n
n
for which there exist integers
a
1
,
a
2
,
…
,
a
n
a_1, a_2,\ldots, a_n
a
1
,
a
2
,
…
,
a
n
such that quadratic trinom
x
2
−
2
(
a
1
+
a
2
+
⋯
+
a
n
)
2
x
+
(
a
1
4
+
a
2
4
+
⋯
+
a
n
4
+
1
)
x^2-2(a_1+a_2+\cdots+a_n)^2x+(a_1^4+a_2^4+\cdots+a_n^4+1)
x
2
−
2
(
a
1
+
a
2
+
⋯
+
a
n
)
2
x
+
(
a
1
4
+
a
2
4
+
⋯
+
a
n
4
+
1
)
has at least one integral root.
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