Geodesic
On the Diophantine equation z2 = x4 + Dx2y2 + y4
Glasgow mathematical journal, Tome 36 (1994) no. 3, pp. 283-285

Voir la notice de l'article provenant de la source Cambridge University Press

The equation of the title in positive integers x, y, z where D is a given integer has been considered for some 300 years [4, pp 634–639]. As observed by V. A. Lebesgue, and probably known to Euler, if x, y, z is one non-trivial solution i.e., one with xy(x2 – y2) ≠0, another is given by . It then follows that there are infinitely many such with (x, y) = 1. The question that remains is to determine for which values of D such solutions exist. 
Cohn, J. H. E. On the Diophantine equation z2 = x4 + Dx2y2 + y4. Glasgow mathematical journal, Tome 36 (1994) no. 3, pp. 283-285. doi: 10.1017/S001708950003086X
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