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2023 IMC
3
Polynomial equation
Polynomial equation
Source: 2023 IMC #3
August 2, 2023
algebra
polynomial
IMC
functional equation
IMC 2023
Problem Statement
Find all polynomials
P
P
P
in two variables with real coefficients satisfying the identity
P
(
x
,
y
)
P
(
z
,
t
)
=
P
(
x
z
ā
y
t
,
x
t
+
y
z
)
.
P(x,y)P(z,t)=P(xz-yt,xt+yz).
P
(
x
,
y
)
P
(
z
,
t
)
=
P
(
x
z
ā
y
t
,
x
t
+
yz
)
.
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