Geodesic
The Diophantine equation x2+3 = yn
Glasgow mathematical journal, Tome 35 (1993) no. 2, pp. 203-206

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

Many special cases of the equation x2+C= yn where x and y are positive integers and n≥3 have been considered over the years, but most results for general n are of fairly recent origin. The earliest reference seems to be an assertion by Fermat that he had shown that when C=2, n=3, the only solutions are given by x = 5, y = 3; a proof was published by Euler [1]. The first result for general n is due to Lebesgue [2] who proved that when C = 1 there are no solutions. Nagell [4] generalised Fermat's result and proved that for C = 2 the equation has no solution other than x = 5, y = 3, n = 3. He also showed [5] that for C = 4 the equation has no solution except x = 2, y = 2, n = 3 and x = 11, y = 5, n = 3, and claims in [6] to have dealt with the case C = 5. The case C = -1 was solved by Chao Ko, and an account appears in [3], pp. 302–304. 
Cohn, J. H. E. The Diophantine equation x2+3 = yn. Glasgow mathematical journal, Tome 35 (1993) no. 2, pp. 203-206. doi: 10.1017/S0017089500009757
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