MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - Middle School Tournaments
LMT
2020 LMT Spring
4
4
Part of
2020 LMT Spring
Problems
(1)
Spring 2020 Team Round Problem 4
Source:
8/22/2020
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
.