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Given a multivariate quadratic polynomial system in a finite field Fq, the problem MAX-MQ is to find a solution satisfying the maximal number of equations. We prove that the probability of a random assignment satisfying a non-degenerate quadratic equation is at least 1q−O(q−n2), where n is the number of the variables in the equation. Consequently, the random assignment provides a polynomial-time approximation...
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