Geodesic
Experimental program estimation for the quantity of prime numbers necessary for elimination of polynomial equations without integer roots
Prikladnaâ diskretnaâ matematika, no. 10 (2009), pp. 84-87.

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This work deals with a way of eliminating polynomial equations in a single unknown without integer roots with their right parts' known spectrum determined by estimation based on the difference between the polynom's maximum and minimum values in a certain interval. Ideas introduced by Gauss and developed to the case of any prime numbers and any residues were used to elaborate this method. The solutions of congruence in a single variable which demonstrate the elimination method potential are also given. A program in the packet of symbolic calculations is offered for the experimental estimation of the necessary length of the prime numbers list used for equation elimination. The use of a shorter list allows to expect the algorithm's time complexity reduction when this elimination is applied. 
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     title = {Experimental program estimation for the quantity of prime numbers necessary for elimination of polynomial equations without integer roots},
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Yu. L. Zachesov; N. P. Salikhov. Experimental program estimation for the quantity of prime numbers necessary for elimination of polynomial equations without integer roots. Prikladnaâ diskretnaâ matematika, no. 10 (2009), pp. 84-87. http://geodesic.mathdoc.fr/item/PDM_2009_10_a43/

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