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Poland - Second Round
1994 Poland - Second Round
1
1
Part of
1994 Poland - Second Round
Problems
(1)
5-degree polynomial such that (x-1)^3| P(x)+1 and (x+1)^3| P(x)-1
Source: Polish second round 1994 p1
1/19/2020
Find all real polynomials
P
(
x
)
P(x)
P
(
x
)
of degree
5
5
5
such that
(
x
−
1
)
3
∣
P
(
x
)
+
1
(x-1)^3| P(x)+1
(
x
−
1
)
3
∣
P
(
x
)
+
1
and
(
x
+
1
)
3
∣
P
(
x
)
−
1
(x+1)^3| P(x)-1
(
x
+
1
)
3
∣
P
(
x
)
−
1
.
algebra
polynomial
polynomial division