Geodesic
ON THE DIOPHANTINE EQUATION x2 + d2l + 1 = yn
Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 415-428

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DOI

Let d > 0 be a squarefree integer and denote by h = h(−d) the class number of the imaginary quadratic field . It is well known (see e.g. [25]) that for a given positive integer N there are only finitely many squarefree d's for which h(−d) = N. In [45], Saradha and Srinivasan and in [28] Le and Zhu considered the equation in the title and solved it completely under the assumption h(−d) = 1 apart from the case d ≡ 7 (mod 8) in which case y was supposed to be odd. We investigate the title equation in unknown integers (x, y, l, n) with x ≥ 1, y ≥ 1, n ≥ 3, l ≥ 0 and gcd(x, y) = 1. The purpose of this paper is to extend the above result of Saradha and Srinivasan to the case h(−d) ∈ {2, 3}.
DOI : 10.1017/S0017089512000067
Mots-clés : 11D41, 11D61 
BÉRCZES, ATTILA; PINK, ISTVÁN. ON THE DIOPHANTINE EQUATION x2 + d2l + 1 = yn. Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 415-428. doi: 10.1017/S0017089512000067
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     title = {ON {THE} {DIOPHANTINE} {EQUATION} x2 + d2l + 1 = yn},
     journal = {Glasgow mathematical journal},
     pages = {415--428},
     year = {2012},
     volume = {54},
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