Linear congruences with ratios
نویسندگان
چکیده
منابع مشابه
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...
متن کاملParametric 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...
متن کاملCongruences Involving Sums of Ratios of Lucas Sequences
Given a pair (Ut) and (Vt) of Lucas sequences, we establish various congruences involving sums of ratios Vt Ut . More precisely, let p be a prime divisor of the positive integer m. We establish congruences, modulo powers of p, for the sum ∑ Vt Ut , where t runs from 1 to r(m), the rank of m, and r(q) ∤ t for all prime factors q of m.
متن کاملAll Linear-Time Congruences for Familiar Operators
The detailed behaviour of a system is often represented as a labelled transition system (LTS) and the abstract behaviour as a stuttering-insensitive semantic congruence. Numerous congruences have been presented in the literature. On the other hand, there have not been many results proving the absence of more congruences. This publication fully analyses the linear-time (in a well-defined sense) ...
متن کاملThe Lattice of Congruences of a Finite Linear Frame
Let F = 〈F,R〉 be a finite Kripke frame. A congruence of F is a bisimulation of F that is also an equivalence relation on F. The set of all congruences of F is a lattice under the inclusion ordering. In this article we investigate this lattice in the case that F is a finite linear frame. We give concrete descriptions of the join and meet of two congruences with a nontrivial upper bound. Through ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2016
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/12949