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Question: Looking for the difference of cubes

Question:Looking for the difference of cubes

Alfred_F 720 Maple
number-theory
13 hours ago
2

Let B and D be natural numbers. Prove that in the rational numbers there exist solutions (x;y) of the equation x^3-y^3=B^3+D^3 and the equation x^3-y^3=B^3-D^3, and find the solution formula and example solutions.

edited:

This problem becomes interesting when one searches for positive rational solutions x=x(B,D) and y=y(B,D).
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