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Quartic, octic residues and Lucas sequences
- Source :
-
Journal of Number Theory . Mar2009, Vol. 129 Issue 3, p499-550. 52p. - Publication Year :
- 2009
-
Abstract
- Abstract: Let be a prime and with . Suppose for some integers x and y. In the paper we develop the calculation technique of quartic Jacobi symbols and use it to determine . As applications we obtain the congruences for modulo p and the criteria for (if ), where is the Lucas sequence given by , and . We also pose many conjectures concerning , or . [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICS
*SCIENCE
*MATHEMATICAL ability
*MATHEMATICAL programming
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 129
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 36249396
- Full Text :
- https://doi.org/10.1016/j.jnt.2008.09.019