Given an irreducible conic C in PG(2, q) with q odd, how many points of another irreducible conic D in PG(2, q) are external to C? It is not hard to find D such that either all its points off C are external to C, or none of its points are. Apart from these cases, we prove that for q large enough, the number we seek differs from 1 2 (q − 1) by at most √ q + 3.
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