MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2021 Harvard-MIT Mathematics Tournament.
3
2021 Algebra/NT #3: Polynomial with two known points
2021 Algebra/NT #3: Polynomial with two known points
Source:
May 30, 2021
algebra
polynomial
number theory
Problem Statement
Among all polynomials
P
(
x
)
P(x)
P
(
x
)
with integer coefficients for which
P
(
−
10
)
=
145
P(-10) = 145
P
(
−
10
)
=
145
and
P
(
9
)
=
164
P(9) = 164
P
(
9
)
=
164
, compute the smallest possible value of
∣
P
(
0
)
∣
.
|P(0)|.
∣
P
(
0
)
∣.
Back to Problems
View on AoPS