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1984 Vietnam National Olympiad
2
Polynomial satisfying xP(x - a) = (x - b)P(x) for given a,b.
Polynomial satisfying xP(x - a) = (x - b)P(x) for given a,b.
Source: Vietnam MO 1984 P5
March 20, 2011
algebra
polynomial
algebra unsolved
Problem Statement
Given two real numbers
a
,
b
a, b
a
,
b
with
a
≠
0
a \neq 0
a
=
0
, find all polynomials
P
(
x
)
P(x)
P
(
x
)
which satisfy
x
P
(
x
−
a
)
=
(
x
−
b
)
P
(
x
)
.
xP(x - a) = (x - b)P(x).
x
P
(
x
−
a
)
=
(
x
−
b
)
P
(
x
)
.
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