Non-negative integer linear congruences

Restricted linear congruences

In this paper, using properties of Ramanujan sums and of the finite Fourier transform of arithmetic functions, we give an explicit formula for the number of solutions of the linear congruence a1x1 + · · · + akxk ≡ b (mod n), with (xi, n) = ti (1 ≤ i ≤ k), where a1, t1, . . . , ak, tk, b, n (n ≥ 1) are arbitrary integers. Some special cases of this problem have been studied in many papers, and h...

Application-oriented mixed integer non-linear programming

A Non-linear Integer Bi-level Programming Model for Competitive Facility Location of Distribution Centers

The facility location problem is a strategic decision-making for a supply chain, which determines the profitability and sustainability of its components. This paper deals with a scenario where two supply chains, consisting of a producer, a number of distribution centers and several retailers provided with similar products, compete to maintain their market shares by opening new distribution cent...

Parametric Systems of Linear Congruences

Based on an extended quantifier elimination procedure for discretely valued fields, we devise algorithms for solving multivariate systems of linear congruences over the integers. This includes determining integer solutions for sets of moduli which are all power of a fixed prime, uniform p-adic integer solutions for parametric prime power moduli, lifting strategies for these uniform p-adic solut...

on the effect of linear & non-linear texts on students comprehension and recalling

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