On the matricial version of Fermat-Euler congruences

DOI10.1007/s11537-006-0501-6zbMath1168.05003OpenAlexW4255559824MaRDI QIDQ1000312

Vladimir I. Arnold

Publication date: 6 February 2009

Published in: Japanese Journal of Mathematics. 3rd Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11537-006-0501-6

zbMATH Keywords

symmetric functionsmultinomial coefficientsCesaro averagingEuler congruencesNewton-Girard formulalittle Fermat theorem

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07) Matrices, determinants in number theory (11C20)

Related Items (9)

Fermat's Little Theorem and Gauss Congruence: Matrix Versions and Cyclic Permutations ⋮ On the variation of Frobenius eigenvalues in a skew-abelian Iwasawa tower ⋮ Generalizations of Arnold's version of Euler's theorem for matrices ⋮ Representations of analytic functions as infinite products and their application to numerical computations ⋮ On matrix analogs of Fermat's little theorem ⋮ On some number-theoretic conjectures of V. Arnold ⋮ On congruences for the traces of powers of some matrices ⋮ Extended Euler congruence ⋮ Dold sequences, periodic points, and dynamics

Cites Work

• Empirical estimates of the average orders of orbits period lengths in Euler groups
• Fermat dynamics, matrix arithmetics, finite circles, and finite Lobachevsky planes
• A Coloring Proof of a Generalisation of Fermat's Little Theorem
• Unnamed Item

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