Euler Four-Square Identity -- from Wolfram MathWorld

The amazing polynomial identity communicated by Euler in a letter to Goldbach on April 12, 1749 (incorrectly given as April 15, 1705--before Euler was born--in Conway and Guy 1996, p. 232). The identity also follows from the fact that the norm of the product of two quaternions is the product of the norms (Conway and Guy 1996).

Euler's four-square identity - Wikipedia

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Euler Transform -- from Wolfram MathWorld

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Euler Formula -- from Wolfram MathWorld

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Prove that Euler's four-square identity, Pfister's identity