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Contests
National and Regional Contests
Korea Contests
Korea Winter Program Practice Test
2020 Korean MO winter camp
#6
#6
Part of
2020 Korean MO winter camp
Problems
(1)
Integer sequence and divisibility
Source: 2020 Korean MO winter camp Test 1 P6
9/7/2020
Find all strictly increasing sequences
{
a
n
}
n
=
0
∞
\{a_n\}_{n=0}^\infty
{
a
n
}
n
=
0
∞
of positive integers such that for all positive integers
k
,
m
,
n
k,m,n
k
,
m
,
n
a
n
+
1
+
a
n
+
2
+
⋯
+
a
n
+
k
k
+
m
\frac{a_{n+1} +a_{n+2} +\dots +a_{n+k}}{k+m}
k
+
m
a
n
+
1
+
a
n
+
2
+
⋯
+
a
n
+
k
is not an integer larger than
2020
2020
2020
.
number theory