MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2023 Harvard-MIT Mathematics Tournament
7
2023 Algebra NT #7 a+b = c+d
2023 Algebra NT #7 a+b = c+d
Source:
February 28, 2024
number theory
Problem Statement
If
a
,
b
,
c
a, b, c
a
,
b
,
c
, and
d
d
d
are pairwise distinct positive integers that satisfy
l
c
m
(
a
,
b
,
c
,
d
)
<
1000
lcm (a, b, c, d) < 1000
l
c
m
(
a
,
b
,
c
,
d
)
<
1000
and
a
+
b
=
c
+
d
a+b = c+d
a
+
b
=
c
+
d
, compute the largest possible value of
a
+
b
a + b
a
+
b
.
Back to Problems
View on AoPS