Results 11 to 20 of about 983 (218)
Efficient solution of linear diophantine equations [PDF]
Journal of Symbolic Computation, 1989 The paper gives a new method for finding complete information about all nonnegative solutions of a linear homogeneous or inhomogeneous diophantine equation \[ \sum_{i=1}^{m}a_ix_i- \sum_{j=1}^{n}b_jy_j=c, \] where the \(a_i's\) and \(b_j's\) are positive integers and \(c\) is \(0\) resp. a positive integer.
Michael Clausen, Albrecht Fortenbacher
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Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations [PDF]
Formal Methods in System Design, 2008 Abstract: "The use of Craig interpolants has enabled the development of powerful hardware and software model checking techniques. Efficient algorithms are known for computing interpolants in rational and real linear arithmetic. We focus on subsets of integer linear arithmetic.
Himanshu Jain +2 more
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On Linear Diophantine Equation [PDF]
, 2017 {"references": ["1.\tDickson. L. E, History of the Theory of Numbers, Vol.2, Chelsea, New York, 1952. 2.\tKirch. A. M, Elementary Number Theory, In tent Educational \tpublisher, New York, 1974. 3.\tNagell. T, Introduction to Number Theory, Stockholm and New York, 1951. 4.\tOre. O, Number Theory and its History, McGraw \u2013 Hill. New York. 1948. 5.\
Dr. D. Ramprasad
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Solving Linear Diophantine Equations And Linear Congruential Equations [PDF]
, 2012 This report represents GCD, euclidean algorithm, linear diophantine equation and linear congruential equation. It investigates the methods for solving linear diophantine equations and linear congruential equations in several variables. There are many examples which illustrate the methods for solving equations.
Yesilyurt, Deniz
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Existence and representation of diophantine and mixed diophantine solutions to linear equations and inequalities [PDF]
Discrete Mathematics, 1975 AbstractIn this paper we present necessary and sufficient conditions for the existence of solutions to more general systems of linear diophantine equations and inequalities than have previously been considered. We do this in terms of variants and extensions of generalized inverse concepts which also permit us to give representation of the set of all ...
Abraham Charnes, Frieda Granot
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Repdigits in the base $b$ as sums of four balancing numbers [PDF]
Mathematica Bohemica, 2021 The sequence of balancing numbers $(B_n)$ is defined by the recurrence relation $B_n=6B_{n-1}-B_{n-2}$ for $n\geq2$ with initial conditions $B_0=0$ and $B_1=1.$ $B_n$ is called the $n$th balancing number. In this paper, we find all repdigits in the base $
Refik Keskin, Fatih Erduvan
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Matrix Diophantine equations over quadratic rings and their solutions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The method for solving the matrix Diophantine equations over quadratic rings is developed. On the basic of the standard form of matrices over quadratic rings with respect to $(z,k)$-equivalence previously established by the authors, the matrix ...
N.B. Ladzoryshyn +2 more
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Integral geometry on discrete matrices
Moroccan Journal of Pure and Applied Analysis, 2021 In this note, we study the Radon transform and its dual on the discrete matrices by defining hyperplanes as being infinite sets of solutions of linear Diophantine equations. We then give an inversion formula and a support theorem.
Attioui Abdelbaki
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S-Restricted Compositions Revisited [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years.
Behrouz Zolfaghari +2 more
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A New Algorithm Based on Colouring Arguments for Identifying Impossible Polyomino Tiling Problems
Algorithms, 2022 Checkerboard colouring arguments for proving that a given collection of polyominoes cannot tile a finite target region of the plane are well-known and typically applied on a case-by-case basis. In this article, we give a systematic mathematical treatment
Marcus R. Garvie, John Burkardt
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