Abstract: In this work we obtain a nontrivial estimate for the size of the set of triples (a, b, c) ? F?q × Fq × Fq which correspond to stable quadratic polynomials f (X) = aX2 + b X + c over the finite field Fq with q odd. This estimate is an improvement of the bound O(q11/4) conjectured in a recent work of A. Ostafe and I. Shparlinski.

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