Geodesic
On the fourth-powerfree part of x2 + 2
Glasgow mathematical journal, Tome 40 (1998) no. 3, pp. 299-310

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

We show that x = 59 is the largest positive integer for which the fourth-powerfree part of x2 + 2 is at most 100. This implies the solution of the problem, posed recently by J. H. E. Cohn, to prove that (x, y) = (1, 1) is the only solution in nonnegative integers to the diophantine equation x2 – 3y4 = –2, as well as a new solution to the problem, posed a long time ago by the same J. H. E. Cohn and solved before by R. Bumby and N. Tzanakis, to prove that (x, y) = (1, 1), (11, 3) are the only solutions in nonnegative integers to the diophantine equation 2x2 – 3y4 = – 1. 
Weger, Benjamin M. M. de. On the fourth-powerfree part of x2 + 2. Glasgow mathematical journal, Tome 40 (1998) no. 3, pp. 299-310. doi: 10.1017/S0017089500032651
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