MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
BMT Problems
2022 BMT
6
BMT 2022 Fall Algebra P6
BMT 2022 Fall Algebra P6
Source:
May 5, 2023
algebra
functions
Problem Statement
The degree-
6
6
6
polynomial
f
f
f
satisfies
f
(
7
)
−
f
(
1
)
=
1
,
f
(
8
)
−
f
(
2
)
=
16
,
f
(
9
)
−
f
(
3
)
=
81
,
f
(
10
)
−
f
(
4
)
=
256
f(7) - f(1) = 1, f(8) - f(2) = 16, f(9) - f(3) = 81, f(10) - f(4) = 256
f
(
7
)
−
f
(
1
)
=
1
,
f
(
8
)
−
f
(
2
)
=
16
,
f
(
9
)
−
f
(
3
)
=
81
,
f
(
10
)
−
f
(
4
)
=
256
and
f
(
11
)
−
f
(
5
)
=
625.
f(11) - f(5) = 625.
f
(
11
)
−
f
(
5
)
=
625.
Compute
f
(
15
)
−
f
(
−
3
)
.
f(15) - f(-3).
f
(
15
)
−
f
(
−
3
)
.
Back to Problems
View on AoPS