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Canada National Olympiad
2013 Canada National Olympiad
1
Polynomial Equation
Polynomial Equation
Source: 2013 CMO #1
March 31, 2013
algebra
polynomial
Vieta
algebra unsolved
Problem Statement
Determine all polynomials
P
(
x
)
P(x)
P
(
x
)
with real coefficients such that
(
x
+
1
)
P
(
x
−
1
)
−
(
x
−
1
)
P
(
x
)
(x+1)P(x-1)-(x-1)P(x)
(
x
+
1
)
P
(
x
−
1
)
−
(
x
−
1
)
P
(
x
)
is a constant polynomial.
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