MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
CHMMC problems
2018 CHMMC (Fall)
9
9
Part of
2018 CHMMC (Fall)
Problems
(1)
2018 Fall Team #9
Source:
4/17/2022
Say that a function
f
:
{
1
,
2
,
.
.
.
,
1001
}
→
Z
f : \{1, 2, . . . , 1001\} \to Z
f
:
{
1
,
2
,
...
,
1001
}
→
Z
is almost polynomial if there is a polynomial
p
(
x
)
=
a
200
x
200
+
.
.
.
+
a
1
x
+
a
0
p(x) = a_{200}x^{200} +... + a_1x + a_0
p
(
x
)
=
a
200
x
200
+
...
+
a
1
x
+
a
0
such that each an is an integer with
∣
a
n
∣
≤
201
|a_n| \le 201
∣
a
n
∣
≤
201
, and such that
∣
f
(
x
)
−
p
(
x
)
∣
≤
1
|f(x) - p(x)| \le 1
∣
f
(
x
)
−
p
(
x
)
∣
≤
1
for all
x
∈
{
1
,
2
,
.
.
.
,
1001
}
x \in \{1, 2, . . . , 1001\}
x
∈
{
1
,
2
,
...
,
1001
}
. Let
N
N
N
be the number of almost polynomial functions. Compute the remainder upon dividing
N
N
N
by
199
199
199
.
algebra