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2012 IMO Shortlist
N2
IMO Shortlist 2012, Number Theory 2
IMO Shortlist 2012, Number Theory 2
Source: IMO Shortlist 2012, Number Theory 2
July 29, 2013
algebra
number theory
IMO Shortlist
Problem Statement
Find all triples
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of positive integers such that
x
≤
y
≤
z
x \leq y \leq z
x
≤
y
≤
z
and
x
3
(
y
3
+
z
3
)
=
2012
(
x
y
z
+
2
)
.
x^3(y^3+z^3)=2012(xyz+2).
x
3
(
y
3
+
z
3
)
=
2012
(
x
yz
+
2
)
.
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