MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2013 Harvard-MIT Mathematics Tournament
30
2013 HMMT Guts #30: Solutions to LCM Equation
2013 HMMT Guts #30: Solutions to LCM Equation
Source:
March 26, 2013
HMMT
number theory
least common multiple
Problem Statement
How many positive integers
k
k
k
are there such that
k
2013
(
a
+
b
)
=
l
c
m
(
a
,
b
)
\dfrac k{2013}(a+b)=lcm(a,b)
2013
k
(
a
+
b
)
=
l
c
m
(
a
,
b
)
has a solution in positive integers
(
a
,
b
)
(a,b)
(
a
,
b
)
?
Back to Problems
View on AoPS