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Question: In memory of IMO 1988

Question:In memory of IMO 1988

Alfred_F 85 Maple 2024
diophantine_equation numbrix-puzzle
September 30 2024
3

A task that was famous at the time is worth remembering:

If for whole numbers x and y the number N = (x^2+y^2)/(1+x*y) is a positive whole number, then it is also a square number.

It can be proven that the converse is also true. Therefore, here is the task:

If N is a square number, then the Diophantine equation has solutions. Solutions must be calculated for N = 9, 49 and 729.
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