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2021 MMATHS
9
9
Part of
2021 MMATHS
Problems
(1)
MMATHS 2021, Problem 9
Source:
10/31/2021
Suppose that
P
(
x
)
P(x)
P
(
x
)
is a monic cubic polynomial with integer roots, and suppose that
P
(
a
)
a
\frac{P(a)}{a}
a
P
(
a
)
is an integer for exactly
6
6
6
integer values of
a
a
a
. Suppose furthermore that exactly one of the distinct numbers
P
(
1
)
+
P
(
−
1
)
2
\frac{P(1) + P(-1)}{2}
2
P
(
1
)
+
P
(
−
1
)
and
P
(
1
)
−
P
(
−
1
)
2
\frac{P(1) - P(-1)}{2}
2
P
(
1
)
−
P
(
−
1
)
is a perfect square. Given that
P
(
0
)
>
0
P(0) > 0
P
(
0
)
>
0
, find the second-smallest possible value of
P
(
0
)
.
P(0).
P
(
0
)
.
Proposed by Andrew Wu
Yale
MMATHS