MathDB
Problems
Contests
National and Regional Contests
Serbia Contests
Serbia Team Selection Test
2018 Serbia Team Selection Test
6
Is a linear combination of 2018th power bounded?
Is a linear combination of 2018th power bounded?
Source: Serbia TST 2018 P6
May 29, 2018
algebra
combinatorics
Problem Statement
For any positive integer
n
n
n
, define
c
n
=
min
(
z
1
,
z
2
,
.
.
.
,
z
n
)
∈
{
−
1
,
1
}
n
∣
z
1
⋅
1
2018
+
z
2
⋅
2
2018
+
.
.
.
+
z
n
⋅
n
2018
∣
.
c_n=\min_{(z_1,z_2,...,z_n)\in\{-1,1\}^n} |z_1\cdot 1^{2018} + z_2\cdot 2^{2018} + ... + z_n\cdot n^{2018}|.
c
n
=
(
z
1
,
z
2
,
...
,
z
n
)
∈
{
−
1
,
1
}
n
min
∣
z
1
⋅
1
2018
+
z
2
⋅
2
2018
+
...
+
z
n
⋅
n
2018
∣.
Is the sequence
(
c
n
)
n
∈
Z
+
(c_n)_{n\in\mathbb{Z}^+}
(
c
n
)
n
∈
Z
+
bounded?
Back to Problems
View on AoPS