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International Zhautykov Olympiad
2014 International Zhautykov Olympiad
1
Polynom
Polynom
Source:
January 15, 2014
algebra
polynomial
calculus
integration
algebra proposed
Problem Statement
Does there exist a polynomial
P
(
x
)
P(x)
P
(
x
)
with integral coefficients such that
P
(
1
+
3
)
=
2
+
3
P(1+\sqrt 3) = 2+\sqrt 3
P
(
1
+
3
)
=
2
+
3
and
P
(
3
+
5
)
=
3
+
5
P(3+\sqrt 5) = 3+\sqrt 5
P
(
3
+
5
)
=
3
+
5
?Proposed by Alexander S. Golovanov, Russia
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