MathDB
Problems
Contests
National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2014 Switzerland - Final Round
2
2
Part of
2014 Switzerland - Final Round
Problems
(1)
Perfect Square
Source: Switzerland Math Olympiad, Final round 2014, P2
6/2/2014
Let
a
,
b
∈
N
a,b\in\mathbb{N}
a
,
b
∈
N
such that :
a
b
(
a
−
b
)
∣
a
3
+
b
3
+
a
b
ab(a-b)\mid a^3+b^3+ab
ab
(
a
−
b
)
∣
a
3
+
b
3
+
ab
Then show that
lcm
(
a
,
b
)
\operatorname{lcm}(a,b)
lcm
(
a
,
b
)
is a perfect square.
number theory
least common multiple
number theory proposed