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
Full paper (PDF, 103 Kb)

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Authors and affiliations

Mickey Polasub
9/34 Ramintra 40 Rd.
Nuanchan, Beungkum, Bangkok, Thailand 10230

Abstract

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

Keywords

• Exponential diophantine equations
• Primitive divisors

AMS Classification

• Primary: 11D61

References

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 +5^k17^l = yⁿ, Communications in Math., Vol. 19, 2011, 1–9.
3. Virgolici, H. On the exponential diophantine equation 2^x +1009^y = p^z, Analele Univ. Spiru Haret – Seria Mat.-Inf., Vol. 7, 2011, 1–9.