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Contests
National and Regional Contests
India Contests
India IOQM
2024-25 IOQM India
24
IOQM P24 2024
IOQM P24 2024
Source:
September 8, 2024
algebra
polynomial
Problem Statement
Consider the set
F
F
F
of all polynomials whose coefficients are in the set of
{
0
,
1
}
\{0,1\}
{
0
,
1
}
. Let
q
(
x
)
=
x
3
+
x
+
1
q(x) = x^3 + x +1
q
(
x
)
=
x
3
+
x
+
1
. The number of polynomials
p
(
x
)
p(x)
p
(
x
)
in
F
F
F
of degree
14
14
14
such that the product
p
(
x
)
q
(
x
)
p(x)q(x)
p
(
x
)
q
(
x
)
is also in
F
F
F
is:
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