MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Princeton University Math Competition
2008 Princeton University Math Competition
A9/B10
2008 PUMaC Algebra A9 / B10
2008 PUMaC Algebra A9 / B10
Source:
September 24, 2019
algebra
Problem Statement
If
p
(
x
)
p(x)
p
(
x
)
is a polynomial with integer coeffcients, let
q
(
x
)
=
p
(
x
)
x
(
1
−
x
)
q(x) = \frac{p(x)}{x(1-x)}
q
(
x
)
=
x
(
1
−
x
)
p
(
x
)
. If
q
(
x
)
=
q
(
1
1
−
x
)
q(x) = q\left(\frac{1}{1-x}\right)
q
(
x
)
=
q
(
1
−
x
1
)
for every
x
≠
0
x \ne 0
x
=
0
, and
p
(
2
)
=
−
7
,
p
(
3
)
=
−
11
p(2) = -7, p(3) = -11
p
(
2
)
=
−
7
,
p
(
3
)
=
−
11
, find
p
(
10
)
p(10)
p
(
10
)
.
Back to Problems
View on AoPS