Journal of Integer Sequences, Vol. 17 (2014), Article 14.11.5

On the Diophantine Equation x4 + y4 + z4 + t4 = w2

Alejandra Alvarado
Eastern Illinois University
Department of Mathematics and Computer Science
600 Lincoln Avenue
Charleston, IL 61920

Jean-Joël Delorme
6 rue des Emeraudes
69006 Lyon


To our knowledge, only three parametric solutions to the equation x4 + y4 + z4 + t4 = w2 were previously known. In this paper, we study the equation x4 + y4 + z4 + t4 = (x2 + y2 + z2 - t2)2. We prove that it is possible to obtain infinitely many parametric solutions by finding points on an elliptic curve over a field Q(m) and we give several new parametric solutions.

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Received August 11 2014; revised version received October 5 2014. Published in Journal of Integer Sequences, November 7 2014.

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