[math-fun] Still an open problem?

Euler had published the complete parametric solution in rationals of x^3 + y^3 = z^3 + w^3 (1) but as said by Hardy and Wright in their book: "The problem of finding all integral solutions is more difficult". In the Rocky Mountain Journal of Mathematics, 1998, Ajai Choudhry published a "complete" parametric solution in integers of (1). But it seems that some number theorists don't agree with this solution or any other claimed solution. Do you know if the complete parametric solution in integers of (1) is still an open problem? Christian.