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Integer solutions of the diophantine equation A4 + hB4 = C4 + hD4 are known for all positive integer values of h < 1000. While a solution of the aforementioned diophantine equation for any arbitrary positive integer value of h is not known, Gerardin and Piezas found solutions of this equation when h is given by polynomials of degrees 5 and 2, respectively. In this paper, we present several new solutions of this equation when h is given by polynomials of degrees 2, 3 and 4.
- Fourth powers
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Cite this paper
Choudhry, A. (2017). A note on the quartic Diophantine equation A4 + hB4 = C4 + hD4. Notes on Number Theory and Discrete Mathematics, 23(1), 1-3.