Results 11 to 20 of about 3,886,089 (197)
On the Number of Nonnegative Solutions to the Inequality a1 +....ar < n [PDF]
, 2010 In this paper, we present a simple and fast method for counting the number of nonnegative integer solutions to the equality a1x1+a2x2+: : :+arxr = n where a1; a2; :::; ar and n are positive integers.
Farzaneh , A. +3 more
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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
, 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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Integral zeroes of Krawtchouk polynomials [PDF]
, 2012 This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.Krawtchouk polynomials appear in many various areas of mathematics starting from discrete mathematics (e.g., in coding theory), association schemes, and in ...
Alenezi, Ahmad M
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Unification and equation solving in nilpotent groups and monoids [PDF]
, 1991 Unification and equation solving have been considered for groups [44], semigroups [43], abelian groups [39] and abelian semigroups [25], [33], [68], [69]. In this thesis we consider partially commutative groups and monoids. Nilpotency provides us with a
Burke, Edmund Kieran, Burke, E.K
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Sparse Solutions of Linear Diophantine Equations [PDF]
SIAM Journal on Applied Algebra and Geometry, 2017 We present structural results on solutions to the Diophantine system $A{\boldsymbol y} = {\boldsymbol b}$, ${\boldsymbol y} \in \mathbb Z^t_{\ge 0}$ with the smallest number of non-zero entries. Our tools are algebraic and number theoretic in nature and include Siegel's Lemma, generating functions, and commutative algebra.
Iskander Aliev +3 more
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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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