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Swedish Mathematical Competition
1981 Swedish Mathematical Competition
3
3
Part of
1981 Swedish Mathematical Competition
Problems
(1)
degree 5 pol, p(x) + 1 is divisible by (x-1)^3, p(x)-1 divisible by (x+1)^3
Source: 1981 Swedish Mathematical Competition p3
3/28/2021
Find all polynomials
p
(
x
)
p(x)
p
(
x
)
of degree
5
5
5
such that
p
(
x
)
+
1
p(x) + 1
p
(
x
)
+
1
is divisible by
(
x
−
1
)
3
(x-1)^3
(
x
−
1
)
3
and
p
(
x
)
−
1
p(x) - 1
p
(
x
)
−
1
is divisible by
(
x
+
1
)
3
(x+1)^3
(
x
+
1
)
3
.
polynomial
divisible
algebra