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1976 IMO Longlists
43
Existence of a polynomial given another special polynomial
Existence of a polynomial given another special polynomial
Source:
January 30, 2011
algebra
polynomial
algebra unsolved
Problem Statement
Prove that if for a polynomial
P
(
x
,
y
)
P(x, y)
P
(
x
,
y
)
, we have
P
(
x
−
1
,
y
−
2
x
+
1
)
=
P
(
x
,
y
)
,
P(x - 1, y - 2x + 1) = P(x, y),
P
(
x
−
1
,
y
−
2
x
+
1
)
=
P
(
x
,
y
)
,
then there exists a polynomial
Φ
(
x
)
\Phi(x)
Φ
(
x
)
with
P
(
x
,
y
)
=
Φ
(
y
−
x
2
)
.
P(x, y) = \Phi(y - x^2).
P
(
x
,
y
)
=
Φ
(
y
−
x
2
)
.
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