MathDB
Problems
Contests
National and Regional Contests
Romania Contests
Romania Team Selection Test
1995 Romania Team Selection Test
4
A sequence of integers
A sequence of integers
Source: Romania TST 1995 Test 3 P4
February 22, 2014
number theory
Problem Statement
Find a sequence of positive integers
f
(
n
)
f(n)
f
(
n
)
(
n
∈
N
n \in \mathbb{N}
n
∈
N
) such that: (i)
f
(
n
)
≤
n
8
f(n) \leq n^8
f
(
n
)
≤
n
8
for any
n
≥
2
n \geq 2
n
≥
2
; (ii) for any distinct
a
1
,
⋯
,
a
k
,
n
a_1, \cdots, a_k, n
a
1
,
⋯
,
a
k
,
n
,
f
(
n
)
≠
f
(
a
1
)
+
⋯
+
f
(
a
k
)
f(n) \neq f(a_1) + \cdots+ f(a_k)
f
(
n
)
=
f
(
a
1
)
+
⋯
+
f
(
a
k
)
.
Back to Problems
View on AoPS