A Note on the Quartic Diophantine Equation $A^4+hB^4=C^4+hD^4$

Abstract: Integer solutions of the diophantine equation

A^{4} + h B^{4} = C^{4} + h D^{4}

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.

This page was built for publication: A Note on the Quartic Diophantine Equation $A^4+hB^4=C^4+hD^4$