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Chile TST Ibero
2023 Chile TST Ibero.
2
Another trivial question
Another trivial question
Source:
October 23, 2024
TST
Chile
algebra
Problem Statement
Consider a function
n
↦
f
(
n
)
n \mapsto f(n)
n
↦
f
(
n
)
that satisfies the following conditions:
f
(
n
)
f(n)
f
(
n
)
is an integer for each
n
n
n
.
f
(
0
)
=
1
f(0) = 1
f
(
0
)
=
1
.
f
(
n
+
1
)
>
f
(
n
)
+
f
(
n
−
1
)
+
⋯
+
f
(
0
)
f(n+1) > f(n) + f(n-1) + \cdots + f(0)
f
(
n
+
1
)
>
f
(
n
)
+
f
(
n
−
1
)
+
⋯
+
f
(
0
)
for each
n
=
0
,
1
,
2
,
…
n = 0, 1, 2, \dots
n
=
0
,
1
,
2
,
…
. Determine the smallest possible value of
f
(
2023
)
f(2023)
f
(
2023
)
.
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