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Girls in Math at Yale
2022 Girls in Math at Yale
9
9
Part of
2022 Girls in Math at Yale
Problems
(1)
Girls in Math at Yale 2022 Problem 9: Monic Quadratics Strike Again
Source:
2/27/2022
Suppose that
P
(
x
)
P(x)
P
(
x
)
is a monic quadratic polynomial satisfying
a
P
(
a
)
=
20
P
(
20
)
=
22
P
(
22
)
aP(a) = 20P(20) = 22P(22)
a
P
(
a
)
=
20
P
(
20
)
=
22
P
(
22
)
for some integer
a
≠
20
,
22
a\neq 20, 22
a
=
20
,
22
. Find the minimum possible positive value of
P
(
0
)
P(0)
P
(
0
)
.Proposed by Andrew Wu(Note: wording changed from original to specify that
a
≠
20
,
22
a \neq 20, 22
a
=
20
,
22
.)
Yale
college
quadratics