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New Zealand Contests
NZMOC Camp Selection Problems
2016 NZMOC Camp Selection Problems
5
5
Part of
2016 NZMOC Camp Selection Problems
Problems
(1)
Q(x) = (x + 1)P(x-1) -(x-1)P(x) is constant
Source: New Zealand NZMOC Camp Selection Problems 2016 p5
9/19/2021
Find all polynomials
P
(
x
)
P(x)
P
(
x
)
with real coefficients such that the polynomial
Q
(
x
)
=
(
x
+
1
)
P
(
x
−
1
)
−
(
x
−
1
)
P
(
x
)
Q(x) = (x + 1)P(x-1) -(x-1)P(x)
Q
(
x
)
=
(
x
+
1
)
P
(
x
−
1
)
−
(
x
−
1
)
P
(
x
)
is constant.
algebra
polynomial