A comment on a result of Virgolici

Mickey Polasub
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 18, 2012, Number 4, Pages 71—72
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Mickey Polasub
9/34 Ramintra 40 Rd.
Nuanchan, Beungkum, Bangkok, Thailand 10230


We provide a short proof of a generalization of a recent result of Virgolici on the diophantine equation 2x + 1009y = pz.


  • Exponential diophantine equations
  • Primitive divisors

AMS Classification

  • Primary: 11D61


  1. Bilu, Y., G. Hanrot, P. Voutier, Existence of primitive divisors of Lucas and Lehmer numbers, J. Reine Angew. Math., Vol. 539, 2001, 75–122.
  2. Pink, I., Z. Rabai, On the diophantine equation x2 +5k17l = yn, Communications in Math., Vol. 19, 2011, 1–9.
  3. Virgolici, H. On the exponential diophantine equation 2x +1009y = pz, Analele Univ. Spiru Haret – Seria Mat.-Inf., Vol. 7, 2011, 1–9.

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Cite this paper

Polasub, M. (2012). A comment on a result of Virgolici. Notes on Number Theory and Discrete Mathematics, 18(4), 71-72.

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