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Integral Solutions to the Equation \(x^2 + y^2 + z^2 = u^2\): A Geometrical Approach

by Ayoub B. Ayoub (Pennsylvania State University)

This article originally appeared in:
Mathematics Magazine
September, 1984

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

Six identities, each of which gives infinitely many (but not all) integral solutions to the equation in the title, are shown to be special cases of a more general identity.

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