Journal of Integer Sequences, Vol. 24 (2021), Article 21.1.8

Four Biquadrates whose Sum is a Perfect Square

Ajai Choudhry
13/4 A Clay Square
Lucknow 226001


All known nontrivial parametric solutions of the diophantine equation x14 + x24 + x34 + x44 = y2 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.

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Received October 9 2020; revised version received January 18 2021. Published in Journal of Integer Sequences, January 23 2021.

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