MathDB
Problems
Contests
National and Regional Contests
Japan Contests
Japan MO Finals
2023 Japan MO Finals
3
3
Part of
2023 Japan MO Finals
Problems
(1)
Weird sequence problem
Source: 2023 Japan MO Finals 3
2/11/2023
Let
c
c
c
be a nonnegative integer. Find all infinite sequences of positive integers
{
a
n
}
n
≥
1
\{a_{n}\}_{n\geq 1}
{
a
n
}
n
≥
1
satisfying the following condition: for all positive integer
n
n
n
, there are exactly
a
n
a_n
a
n
positive integers
i
i
i
such that
a
i
≤
a
n
+
1
+
c
a_i\leq a_{n+1}+c
a
i
≤
a
n
+
1
+
c
.
algebra