Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897139 | Journal of Number Theory | 2018 | 27 Pages |
Abstract
In this work, we give upper bounds for n on the title equation. Our results depend on assertions describing the precise exponents of 2 and 3 appearing in the prime factorization of Tk(x)=(x+1)k+(x+2)k+...+(2x)k. Further, on combining Baker's method with the explicit solution of polynomial exponential congruences (see e.g. [6]), we show that for 2â¤xâ¤13,kâ¥1,yâ¥2 and nâ¥3 the title equation has no solutions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Attila Bérczes, István Pink, Gamze SavaÅ, Gökhan Soydan,