Four Biquadrates whose Sum is a Perfect Square
13/4 A Clay Square
All known nontrivial parametric solutions of the diophantine equation
x14 + x24 + x34 + x44
give the values of xi,
i = 1, ..., 4, in terms of polynomials in two parameters. In the
three simplest solutions, these polynomials are of degrees 2, 4 and 12
respectively. In this paper we obtain infinitely many solutions of the
equation under consideration in terms of quadratic polynomials in two
parameters, as well as a solution in terms of quartic polynomials in
three parameters. We also show how more general multi-parameter solutions
of the equation may be obtained.
Full version: pdf,
Received October 9 2020; revised version received January 18 2021.
Published in Journal of Integer Sequences,
January 23 2021.
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