Linear combinations of prime powers in binary recurrence sequences
نویسندگان
چکیده
منابع مشابه
Products of Prime Powers in Binary Recurrence Sequences
We show how the Gelfond-Baker theory and diophantine approximation techniques can be applied to solve explicitly the diophantine equation G, = wp" ... p', (where (G,, }I='o is a binary recurrence sequence with positive discriminant), for arbitrary values of the parameters. We apply this to the equation x2 + k = ... ps', which is a generalization of the Ramanujan-Nagell equation x2 + 7 = 2Z. We ...
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Let {uk} be a Lucas sequence. A standard technique for determining the perfect powers in the sequence {uk} combines bounds coming from linear forms in logarithms with local information obtained via Frey curves and modularity. The key to this approach is the fact that the equation uk = xn can be translated into a ternary equation of the form ay2 = bx2n + c (with a, b, c ∈ Z) for which Frey curve...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2017
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042117500166