Geodesic
Two exponential Diophantine equations
Glasgow mathematical journal, Tome 39 (1997) no. 2, pp. 231-232

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

In [3], two open problems were whether either of the diophantine equationswith n ∈ Z and f a prime number, is solvable if ω > 3 and 3 √ ω, but in this paper we allow f to be any (rational) integer and also 3 | ω. Equations of this form and more general ones can effectively be solved [5] with an advanced method based on analytical results, but the search limits are usually of enormous size. Here both equations (1) are norm equations in K (√–3): N(a + bp) = fw with p = (√–1 + –3)/2 which makes it possible to treat them arithmetically. 
Dofs, Erik. Two exponential Diophantine equations. Glasgow mathematical journal, Tome 39 (1997) no. 2, pp. 231-232. doi: 10.1017/S0017089500032122
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