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Putnam
1940 Putnam
A5
A5
Part of
1940 Putnam
Problems
(1)
Putnam 1940 A5
Source: Putnam 1940
2/22/2022
Prove that the simultaneous equations
x
4
−
x
2
=
y
4
−
y
2
=
z
4
−
z
2
x^4 -x^2 =y^4 -y^2 =z^4 -z^2
x
4
−
x
2
=
y
4
−
y
2
=
z
4
−
z
2
are satisfied by the points of
4
4
4
straight lines and
6
6
6
ellipses, and by no other points.
Putnam
conics
ellipse