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6
f(x) = (x^2 +x)^2n+1 is irreducible over Z[x]
f(x) = (x^2 +x)^2n+1 is irreducible over Z[x]
Source: Ukrainian TST 1999 p6
February 13, 2020
number theory
Irreducible
polynomial
Problem Statement
Show that for any
n
ā
N
n \in N
n
ā
N
the polynomial
f
(
x
)
=
(
x
2
+
x
)
2
n
+
1
f(x) = (x^2 +x)^{2^n}+1
f
(
x
)
=
(
x
2
+
x
)
2
n
+
1
is irreducible over
Z
[
x
]
Z[x]
Z
[
x
]
.
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