MathDB
Problems
Contests
National and Regional Contests
Chile Contests
Chile TST Ibero
2023 Chile TST Ibero.
3
3
Part of
2023 Chile TST Ibero.
Problems
(1)
Looks scare but no
Source:
10/23/2024
Determine the smallest positive integer
n
n
n
with the following property: for every triple of positive integers
x
,
y
,
z
x, y, z
x
,
y
,
z
, with
x
x
x
dividing
y
3
y^3
y
3
,
y
y
y
dividing
z
3
z^3
z
3
, and
z
z
z
dividing
x
3
x^3
x
3
, it also holds that
(
x
y
z
)
(xyz)
(
x
yz
)
divides
(
x
+
y
+
z
)
n
(x + y + z)^n
(
x
+
y
+
z
)
n
.
TST
Chile
number theory