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4
so many P(1) (2023 HMMT A4)
so many P(1) (2023 HMMT A4)
Source:
February 25, 2023
HMMT
Problem Statement
Suppose
P
(
x
)
P (x)
P
(
x
)
is a polynomial with real coefficients such that
P
(
t
)
=
P
(
1
)
t
2
+
P
(
P
(
1
)
)
t
+
P
(
P
(
P
(
1
)
)
)
P (t) = P (1)t^2 + P (P (1))t + P (P (P (1)))
P
(
t
)
=
P
(
1
)
t
2
+
P
(
P
(
1
))
t
+
P
(
P
(
P
(
1
)))
for all real numbers
t
t
t
. Compute the largest possible value of
P
(
P
(
P
(
P
(
1
)
)
)
)
P(P(P(P(1))))
P
(
P
(
P
(
P
(
1
))))
.
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