A Generalization of Euler's Criterion to Composite Moduli
arXiv:1507.00098
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.
These results appeared in the author's master's thesis \cite{ma00002} and were presented at the Scientific Student Conference of Eötvös Loránd University on Nov. 26, 2003 as a paper titled "Idempotent Numbers and the Solvability of x^k = a (mod m)". The paper was renamed and some revisions were made in May 2015. (Contains 11 pages with 0 figures.)