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Swedish Mathematical Competition
2003 Swedish Mathematical Competition
4
4
Part of
2003 Swedish Mathematical Competition
Problems
(1)
1 + P(x) = 1/2 (P(x -1) + P(x + 1))
Source: 2003 Swedish Mathematical Competition p4
3/21/2021
Determine all polynomials
P
P
P
with real coeffients such that
1
+
P
(
x
)
=
1
2
(
P
(
x
−
1
)
+
P
(
x
+
1
)
)
1 + P(x) = \frac12 (P(x -1) + P(x + 1))
1
+
P
(
x
)
=
2
1
(
P
(
x
−
1
)
+
P
(
x
+
1
))
for all real
x
x
x
.
algebra
polynomial