Geodesic
On the relation between a factorization of a polynomial resultant and the frequency of it’s occurence
Trudy Instituta matematiki, Tome 22 (2014) no. 2, pp. 9-17

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A lower bound is obtained for the number of polynomial pairs of a given degree and bounded heights such that their resultants are divisible by a fixed prime power. 
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N. V. Budarina; V. I. Bernik; H. O'Donnell. On the relation between a factorization of a polynomial resultant and the frequency of it’s occurence. Trudy Instituta matematiki, Tome 22 (2014) no. 2, pp. 9-17. http://geodesic.mathdoc.fr/item/TIMB_2014_22_2_a1/