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Izvestiya: Mathematics, 2004, Volume 68, Issue 6, Pages 1119–1128
DOI: https://doi.org/10.1070/IM2004v068n06ABEH000510 (Mi im510) 		 
This article is cited in 8 scientific papers (total in 9 papers)

The matrix Euler–Fermat theorem

V. I. Arnol'd

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (143 kB) Citations (9)
References:
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DOI: https://doi.org/10.1070/IM2004v068n06ABEH000510
Abstract: We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard–Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem.
Received: 02.03.2004
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2004, Volume 68, Issue 6, Pages 61–70
DOI: https://doi.org/10.4213/im510
Bibliographic databases:
Document Type: Article
UDC: 511
MSC: 11A99, 15A36
Language: English
Original paper language: Russian
Citation: V. I. Arnol'd, “The matrix Euler–Fermat theorem”, Izv. RAN. Ser. Mat., 68:6 (2004), 61–70; Izv. Math., 68:6 (2004), 1119–1128
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM2004v068n06ABEH000510
  • https://www.mathnet.ru/eng/im/v68/i6/p61
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:1741
    Russian version PDF:1080
    English version PDF:130
    References:121
    First page:9
     
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