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
USA
Jean-Joël Delorme
6 rue des Emeraudes
69006 Lyon
France
Abstract:
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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