On equal sums of cubes
The complete solution in positive or negative rationals of the diophantine equation (1) \(x^3+ y^3= u^3+ v^3\) was found by Euler [\textit{G. H. Hardy} and \textit{E. M. Wright}, An introduction to the theory of numbers, 5th ed., Oxford University Press, London 199-200 (1979; Zbl 0423.10001)]. In this paper the author gives a complete solution in positive or negative integers to (1) and to the related equation (2) \(x^3+ y^3+ z^3= t^3\) as well as a complete solution in positive integers only.
scientific article; zbMATH DE number 1309876