Geodesic
On the size of $p$-adic cylinder for which the regular system of algebraic numbers can be constructed
Trudy Instituta matematiki, Tome 22 (2014) no. 2, pp. 96-108.

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On the relation between a factorization of a polynomial resultant and the frequency of its occurrence. 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 number. 
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N. V. Budarina; M. V. Lamchanovskaya. On the size of $p$-adic cylinder for which the regular system of algebraic numbers can be constructed. Trudy Instituta matematiki, Tome 22 (2014) no. 2, pp. 96-108. http://geodesic.mathdoc.fr/item/TIMB_2014_22_2_a9/

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