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Brazil Team Selection Test
2010 Brazil Team Selection Test
2
2
Part of
2010 Brazil Team Selection Test
Problems
(1)
lcm (n, n + 1, n + 2, ... , n + k) > lcm (n + 1, n + 2, n + 3,... , n + k + 1)
Source: 2010 Brazil IMO TST 3.2
7/24/2021
Let
k
>
1
k > 1
k
>
1
be a fixed integer. Prove that there are infinite positive integers
n
n
n
such that
l
c
m
(
n
,
n
+
1
,
n
+
2
,
.
.
.
,
n
+
k
)
>
l
c
m
(
n
+
1
,
n
+
2
,
n
+
3
,
.
.
.
,
n
+
k
+
1
)
.
lcm \, (n, n + 1, n + 2, ... , n + k) > lcm \, (n + 1, n + 2, n + 3,... , n + k + 1).
l
c
m
(
n
,
n
+
1
,
n
+
2
,
...
,
n
+
k
)
>
l
c
m
(
n
+
1
,
n
+
2
,
n
+
3
,
...
,
n
+
k
+
1
)
.
number theory
least common multiple
LCM