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Tuymaada Olympiad
2015 Tuymaada Olympiad
3
3
Part of
2015 Tuymaada Olympiad
Problems
(1)
Polynomial
Source: Tuymaada 2015, Day 1, Problem 3, Senior League
7/10/2017
P
(
x
,
y
)
P(x,y)
P
(
x
,
y
)
is polynomial with real coefficients and
P
(
x
+
2
y
,
x
+
y
)
=
P
(
x
,
y
)
P(x+2y,x+y)=P(x,y)
P
(
x
+
2
y
,
x
+
y
)
=
P
(
x
,
y
)
. Prove that exists polynomial
Q
(
t
)
Q(t)
Q
(
t
)
such that
P
(
x
,
y
)
=
Q
(
(
x
2
ā
2
y
2
)
2
)
P(x,y)=Q((x^2-2y^2)^2)
P
(
x
,
y
)
=
Q
((
x
2
ā
2
y
2
)
2
)
A. Golovanov
algebra
polynomial