József Vass
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 3, Pages 9—19
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Authors and affiliations
József Vass
Department of Algebra and Number Theory, Eötvös Loránd University
Pázmány Péter sétány 1/C, H-1117 Budapest, Hungary
Abstract
A necessary and sufficient condition is provided for the solvability of a binomial congruence with a composite modulus, circumventing its prime factorization. This is a generalization of Euler’s Criterion through that of Euler’s Theorem, and the concepts of order and primitive roots. Idempotent numbers play a central role in this effort.
Keywords
- Binomial congruences
- Power residues
- Generalized primitive roots
AMS Classification
- 11A15
- 11A07
- 11C08
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Cite this paper
Vass, J. (2016). A generalization of Euler’s Criterion to composite moduli. Notes on Number Theory and Discrete Mathematics, 22(3), 9-19.