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LMT
2020 LMT Spring
4
Spring 2020 Team Round Problem 4
Spring 2020 Team Round Problem 4
Source:
August 22, 2020
Problem Statement
Suppose there are
n
n
n
ordered pairs of positive integers
(
a
i
,
b
i
)
(a_i,b_i)
(
a
i
,
b
i
)
such that
a
i
+
b
i
=
2020
a_i+b_i=2020
a
i
+
b
i
=
2020
and
a
i
b
i
a_ib_i
a
i
b
i
is a multiple of
2020
2020
2020
, where
1
≤
i
≤
n
1\le i \le n
1
≤
i
≤
n
. Compute the sum
∑
i
=
1
n
a
i
+
b
i
.
\sum_{i=1}^{n} a_i+b_i.
i
=
1
∑
n
a
i
+
b
i
.
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