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China Girls Math Olympiad
2019 China Girls Math Olympiad
2
2
Part of
2019 China Girls Math Olympiad
Problems
(1)
Chinese Girls Mathematical Olympiad 2019, Problem 2
Source:
8/12/2019
Find integers
a
1
,
a
2
,
⋯
,
a
18
a_1,a_2,\cdots,a_{18}
a
1
,
a
2
,
⋯
,
a
18
, s.t.
a
1
=
1
,
a
2
=
2
,
a
18
=
2019
a_1=1,a_2=2,a_{18}=2019
a
1
=
1
,
a
2
=
2
,
a
18
=
2019
, and for all
3
≤
k
≤
18
3\le k\le 18
3
≤
k
≤
18
, there exists
1
≤
i
<
j
<
k
1\le i<j<k
1
≤
i
<
j
<
k
with
a
k
=
a
i
+
a
j
a_k=a_i+a_j
a
k
=
a
i
+
a
j
.
Integer
algebra
number theory