Irrational numbers - Colegiul Național din Iași (Iași - Roumanie)

Let d  1 be an integer. Determine all numbers of the form a  b (a, b  Z) such that their inverses are of the same form (a  b , with a, b  Z). For instance, for d  2, 1  has this property, since: One can assume d is squarefree (d  0 and 1 and d is not divisible with the square of any prime; d can be 2, 3, 1, 6, ..., but not 8 or 18).