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Problems
Contests
National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2020 Korea Junior Math Olympiad
6
6
Part of
2020 Korea Junior Math Olympiad
Problems
(1)
find the greatest positive integer n
Source: KJMO 2020 p6
9/30/2021
for a positive integer
n
n
n
, there are positive integers
a
1
,
a
2
,
.
.
.
a
n
a_1, a_2, ... a_n
a
1
,
a
2
,
...
a
n
that satisfy these two. (1)
a
1
=
1
,
a
n
=
2020
a_1=1, a_n=2020
a
1
=
1
,
a
n
=
2020
(2) for all integer
i
i
i
,
i
i
i
satisfies
2
≤
i
≤
n
,
a
i
−
a
i
−
1
=
−
2
2\leq i\leq n, a_i-a_{i-1}=-2
2
≤
i
≤
n
,
a
i
−
a
i
−
1
=
−
2
or
3
3
3
. find the greatest
n
n
n
KJMO
KMO