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No Arthmetic Cyclic Quadrilaterals

by Ray Beauregard

This article originally appeared in:
College Mathematics Journal
March, 2006

Subject classification(s): Algebra and Number Theory | Number Theory | Integers
Applicable Course(s): 4.3 Number Theory

Based on the notion of "arithmetic triangles," arithmetic quadrilaterals are defined. It was proved by using an elliptic curve argument that no such quadrilateral can be inscribed on a circle. This capsule provides an elementary proof following the classic ideas of Euler and Fermat.

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Capsule Course Topic(s):
Number Theory | Numbers With Special Forms or Properties
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