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Putnam
2006 Putnam
B1
B1
Part of
2006 Putnam
Problems
(1)
Putnam 2006 B1
Source:
12/4/2006
Show that the curve
x
3
+
3
x
y
+
y
3
=
1
x^{3}+3xy+y^{3}=1
x
3
+
3
x
y
+
y
3
=
1
contains only one set of three distinct points,
A
,
B
,
A,B,
A
,
B
,
and
C
,
C,
C
,
which are the vertices of an equilateral triangle.
Putnam
quadratics
geometry
3D geometry
function
Stanford
college