Abstract
Three series of number-theoretic problems with explicitly defined parameters concerning systems of Diophantine dis-equations with solutions from a given domain are considered. Constraints on these parameters under which any problem of each series is NP-complete are proved. It is proved that for any m and m′ (m 2. It is also proved that if the solution to a system of linear Diophantine dis-equations, each containing exactly three variables, is sought in the domain given by a system of polynomial inequalities that contain an n-dimensional cube and are contained in an n-dimensional parallelepiped symmetric with respect to the point of origin, its consistency problem is NP-complete.
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