Galois Fields, Grobner Bases, N queens

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Hi all. Thank you for taking the time to read this. I am currently studying Grobner Bases and I've been given a problem that I'm struggling to find any resources for. I am interested in find if a certain n for the n queens problem have solutions. Now there are SAT solvers and such which can do this but is a NP search problem. I would like to instead, describe the n queens problem as a set of polynomials. To make this easier, let's say that n is a power of two so I can represent it in a finite field of 2 raised to some power. I could then run a grobner bases test to see if the n has solutions. Could anyone suggest where I can look for information or know anything about this topic to get me started? Thank you again.
 

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