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2010 Estonia Team Selection Test
5
5
Part of
2010 Estonia Team Selection Test
Problems
(1)
P(x, y) = (x^2 + y^2)^k when P(sin t, cos t) = 1
Source: Estonia IMO TST 2010 p5
4/1/2020
Let
P
(
x
,
y
)
P(x, y)
P
(
x
,
y
)
be a non-constant homogeneous polynomial with real coefficients such that
P
(
sin
t
,
cos
t
)
=
1
P(\sin t, \cos t) = 1
P
(
sin
t
,
cos
t
)
=
1
for every real number
t
t
t
. Prove that there exists a positive integer
k
k
k
such that
P
(
x
,
y
)
=
(
x
2
+
y
2
)
k
P(x, y) = (x^2 + y^2)^k
P
(
x
,
y
)
=
(
x
2
+
y
2
)
k
.
polynomial
algebra
trigonometry