Existence of Primitive Divisors of Lucas and Lehmer Numbers

By Yuri F. Bilu, G. Hanrot, P. Voutier. 2001

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Ternary Diophantine Equations via Galois Representations and Modular Forms (2004, methodology): “Techniques to fully solve (8.1), for instance in case D = 1, 2, 3, 4, 5, 6, have traditionally instead relied upon factorizations in Q( √ −D) and straightforward algebraic arguments; recently, the primitive divisor theorem of Bilu, Hanrot and Voutier [3] has played a prominent role (see e.g. [7] and”
On the equation x2+2a⋅3b=yn (2002, background): “[3] as well as a computational result of de Weger [7].”
Primitive divisors in arithmetic dynamics (2007, background): “A recent deep result of Bilu, Hanrot and Voutier [6] extends this to the statement the maxZ(L) ≤ 30 for any nontrivial Lucas or Lehmer sequence L.”
Applications of the Hypergeometric Method to the Generalized Ramanujan-Nagell Equation (2002, methodology): “Lehmer numbers by Bilu, Hanrot and Voutier [ BHV ] almost immediately implies the following”