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Putnam 1940 A5

Source: Putnam 1940

February 22, 2022
Putnamconicsellipse

Problem Statement

Prove that the simultaneous equations x4−x2=y4−y2=z4−z2x^4 -x^2 =y^4 -y^2 =z^4 -z^2 are satisfied by the points of 44 straight lines and 66 ellipses, and by no other points.
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