MathDB
Problems
Contests
National and Regional Contests
Iran Contests
Iran MO (1st Round)
2018 Iran MO (1st Round)
17
17
Part of
2018 Iran MO (1st Round)
Problems
(1)
Find maximum of m+n if lcm(m,n) = (m-n)^2
Source: Iran First Round 2017, P17
3/7/2021
Two positive integers
m
m
m
and
n
n
n
are both less than
500
500
500
and
lcm
(
m
,
n
)
=
(
m
ā
n
)
2
\text{lcm}(m,n) = (m-n)^2
lcm
(
m
,
n
)
=
(
m
ā
n
)
2
. What is the maximum possible value of
m
+
n
m+n
m
+
n
?
number theory
least common multiple