(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 2, PAGES 511-523

## On systems of polynomially solvable linear equations with $k$-valued variables

A. N. Veligura

Abstract

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 A class of polynomially solvable systems of $m$ linear equations of $n$ $k$-valued variables is described. The exact and asymptotic formulae for the cardinal number $\nu_k(n,m)$ of the class are presented. In particular, if $n,m\to \infty$ so that $m/n=(1-1/k)+\omega n^{-1/2}$, where $\omega \to +\infty$ almost all of such systems with columns in general position are polynomially solvable. 

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