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Putnam
1979 Putnam
B3
B3
Part of
1979 Putnam
Problems
(1)
Putnam 1979 B3
Source:
4/8/2022
Let
F
F
F
be a finite field having an odd number
m
m
m
of elements. Let
p
(
x
)
p(x)
p
(
x
)
be an irreducible (i.e. nonfactorable) polynomial over
F
F
F
of the form
x
2
+
b
x
+
c
,
b
,
c
∈
F
.
x^2+bx+c, ~~~~~~ b,c \in F.
x
2
+
b
x
+
c
,
b
,
c
∈
F
.
For how many elements
k
k
k
in
F
F
F
is
p
(
x
)
+
k
p(x)+k
p
(
x
)
+
k
irreducible over
F
F
F
?
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