As a newbie in Maple2024, my next step is to try to solve a Diophantine equation. Attempts with isolve failed. It is the famous task B3 from the IMO of 1988:

If for integers x and y the fraction (x^2+y^2)/(1+x*y) is a positive integer, then it is actually a square number.

The solution is well known. But I would like to learn how to use Maple using this example and would like some advice.

Best regards, Alfred_F

In the attached file I would like to use the functions "Gradient" and "Hessian". Hessian should also calculate the determinant and check positive definiteness. I was unable to do that. Other questions for me as a beginner are:
How are the long brackets and the > sign on the left edge created? What does a semicolon at the end of the command mean? How is a 3D plot created? What does "restart" mean?

Regards, Alfred_FAF_20240831.mwAF_20240831.mw