what will be the shape of the function?

Question

a ^ (n) = c ^ (2) - b ^ (2) for a given a and n there are infinite sets of c and b including terminating decimals for c and b which would be perfect squares like 3 ^ (5) = 122 ^ (2) -121 ^ (2).what will be the shape of the above function a ^ (n) = c ^ (2) - b ^ (2)

Answer 1

For a fixed a and n, and allowing b and c to vary, the curve would be a hyperbolar centered at the origin. You will only be taking the rational points on that curve, though.

Answer 2

you say you have a 2 varible function =>the shape will be a 3D figure
try considering one variable constant and use the theory to draw this restrction