S-Unit Equations in Modules and Linear-Exponential Diophantine Equations [PDF]
Symposium on the Theory of ComputingLet T be a positive integer and M be a finitely presented module over the Laurent polynomial ring ℤ/T[X1±, …, XN±]. We consider S-unit equations over M: these are equations of the form x1 m1 + ⋯ + xK mK = m0, where the variables x1, …, xK range over the ...
Ruiwen Dong, Doron Shafrir
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On the Diophantine equation L-n - L-m=2 . 3(a) [PDF]
, 2019 In this paper we find (n, m, a) solutions of the Diophantine equation L-n - L-m = 2 . 3(a), where L-n and L-m are Lucas numbers with a >= 0 and n > m >= 0.
Bitim, Bahar Demirtürk
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Time-varying Feedback Systems Design Via Diophantine Equation Order Reduction [PDF]
, 2007 Diophantine equation plays an important role in the design and synthesis of feedback compensators. Many methods have been developed to solve the Diophantine equation.
Wu, Shr-Hua
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Performance comparison of quantum-safe multivariate polynomial public key encapsulation algorithm
EURASIP Journal on Information SecurityA novel quantum-safe key encapsulation algorithm, called Multivariate Polynomial Public Key (MPPK), was recently proposed by Kuang, Perepechaenko, and Barbeau.
Randy Kuang +3 more
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On Systems of Linear Diophantine Equations [PDF]
Mathematics Magazine, 1996 Introduction Something happened to me recently I would wager has happened to many who read this note. Teaching a new topic, you cannot understand one of the proofs. Your first attempt to fill the gap fails. You look through your books for an answer. Next, you ask colleagues, go to the library, maybe even use the interlibrary loan. All in vain.
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Finding the General Solution of a Linear Diophantine Equation
The Fibonacci quarterly, 1979 A new procedure for finding the general solution of a linear diophantine equation is given. As a byproduct, the algorithm finds the greatest common divisor (gcd) of a set of integers. Related results and discussion concerning existing procedures are also
S. Morito, H. Salkin
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On Linear Diophantine Equations and Fibonacci Numbers
Journal of Number Theory, 1993 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Hilbert bases of cones related to simultaneous Diophantine approximations and linear Diophantine equations [PDF]
, 1997 This paper investigates properties of the minimal integral solutions of a linear diophantine equation. We present best possible inequalities that must be satisfied by these elements which improves on former results.
Weismantel, Robert, Henk, Martin
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Formulae for the number of non-negative integer solutions of linear Diophantine equation and inequality [PDF]
, 2023 New formulae are presented for the number $P(b)$ of non-negative integer solutions of a Diophantine equation $\sum_{i=1}^{n}a_ix_i=b$ and for the number $Q(b)$ of non-negative integer solutions of the Diophantine inequality $\sum_{i=1}^{n}a_ix_i\leq b$ $(
Samsonadze, Eteri
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Farey sequences and linear diophantine equations [PDF]
, 1993 This thesis introduces the concept of using Farey Sequence in obtaining particular solutions of Linear Diophantine Equations in two unknowns. The relationship between the mediant and adjacent Farey Fractions is shown.The thesis itself is based on the ...
Bautista, Peter Anthony D. +1 more
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