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New bounds and conditions for the equation of Nagell–Ljunggren
- Source :
-
Journal of Number Theory . Jun2007, Vol. 124 Issue 2, p380-395. 16p. - Publication Year :
- 2007
-
Abstract
- Abstract: The general case of the Nagell–Ljunggren equation is and odd primes. In this paper we derive a new bound for which there are no solutions. For small q the problem is harder and we achieve a conditional result: for and some additional condition on must hold. Both functions are quadratic and they leave a small gap for , on which we have no general result. The picture is completed by some explicit, unconditional upper bounds for the absolute values , . [Copyright &y& Elsevier]
- Subjects :
- *QUADRATIC equations
*EQUATIONS
*ALGEBRA
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 124
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 24697593
- Full Text :
- https://doi.org/10.1016/j.jnt.2006.10.010