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NP completeness conditions for verifying the consistency of several kinds of systems of linear diophantine discongruences

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Abstract

We propose two series of number-theory problems with explicitly marked out parameters related to discongruences modulo m. We find parameter constraints that provide the NP completeness for any problem of every series. For any m > 2, we prove the NP completeness of the verification problem for the consistency of a system of linear discongruences modulo m such that any discongruence contains exactly three variables, including the case where its coefficients belong to {–1, 1}. For any m > 3, we prove the NP completeness of the verification problem for the consistency of a system of linear discongruences modulo m such that any discongruence contains exactly 2 variables. If P ≠ NP, then one cannot change the term 2-discongruence for the term 1-discongruence in the statements of the proven theorems.

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Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab. 7–9, St. Petersburg, 199034, Russia

    N. K. Kosovskii, T. M. Kosovskaya & N. N. Kosovskii

Authors
  1. N. K. Kosovskii
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  2. T. M. Kosovskaya
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  3. N. N. Kosovskii
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Correspondence to N. K. Kosovskii.

Additional information

Original Russian Text © N.K. Kosovskii, T.M. Kosovskaya, N.N. Kosovskii, 2016, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2016, No. 1, pp. 25–31.

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Kosovskii, N.K., Kosovskaya, T.M. & Kosovskii, N.N. NP completeness conditions for verifying the consistency of several kinds of systems of linear diophantine discongruences. Vestnik St.Petersb. Univ.Math. 49, 18–22 (2016). https://doi.org/10.3103/S1063454116010088

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  • DOI: https://doi.org/10.3103/S1063454116010088

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