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Putnam
1961 Putnam
A6
Putnam 1961 A6
Putnam 1961 A6
Source: Putnam 1961
June 5, 2022
Putnam
Irreducible
finite fields
Problem Statement
Prove that
p
(
x
)
=
1
+
x
+
x
2
+
…
+
x
n
p(x)=1+x+x^2 +\ldots+x^n
p
(
x
)
=
1
+
x
+
x
2
+
…
+
x
n
is reducible over
F
2
\mathbb{F}_{2}
F
2
in case
n
+
1
n+1
n
+
1
is composite. If
n
+
1
n+1
n
+
1
is prime, is
p
(
x
)
p(x)
p
(
x
)
irreducible over
F
2
\mathbb{F}_{2}
F
2
?
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