Geodesic
On systems of polynomially solvable linear equations with $k$-valued variables
Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 2, pp. 511-523

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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. 
@article{FPM_1998_4_2_a2,
     author = {A. N. Veligura},
     title = {On systems of polynomially solvable linear equations with $k$-valued variables},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {511--523},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1998_4_2_a2/}
}
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A. N. Veligura. On systems of polynomially solvable linear equations with $k$-valued variables. Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 2, pp. 511-523. http://geodesic.mathdoc.fr/item/FPM_1998_4_2_a2/