Kata

In mathematics, a Diophantine equation is a polynomial equation, usually with two or more unknowns, such that only the integer solutions are sought or studied.

In this kata we want to find all integers x, y (x >= 0, y >= 0) solutions of a diophantine equation of the form:

$x^2-4y^2=n\backslash quad\; x^2\; -\; 4y^2\; =\; n$

(where the unknowns are x and y; and n is a given positive number) in decreasing order of the positive $x_{i}x\_i$.

If there is no solution return [] or "[]" or "". (See "RUN SAMPLE TESTS" for examples of returns).

Examples:

90005 --> [[45003, 22501], [9003, 4499], [981, 467], [309, 37]]
90002 --> []

Hint:

$x^2-4y^2=(x-2y)\cdot (x+2y)\backslash quad\; x^2\; -\; 4y^2\; =\; (x\; -\; 2y)\; \backslash cdot\; (x\; +\; 2y)$