Number of small solutions of a homogeneous linear congruence

1991 ◽  
Vol 50 (4) ◽  
pp. 1055-1058 ◽  
Author(s):  
I. A. Semaev
Keyword(s):  
Linear Congruence ◽  
Homogeneous Linear

The number of solutions of a homogeneous linear congruence

2012 ◽  
Vol 153 (3) ◽  
pp. 271-279
Author(s):  
Karol Cwalina ◽  
Tomasz Schoen
Keyword(s):  
Number Of Solutions ◽  
Linear Congruence ◽  
Homogeneous Linear

scholarly journals Note on some representations of general solutions to homogeneous linear difference equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Stevo Stević ◽  
Bratislav Iričanin ◽  
Witold Kosmala ◽  
Zdeněk Šmarda
Keyword(s):  
General Solution ◽  
Difference Equation ◽  
Difference Equations ◽  
Fibonacci Sequence ◽  
Linear Difference Equation ◽  
Linear Difference Equations ◽  
Second Order Difference Equation ◽  
Constant Coefficients ◽  
Order Difference Equation ◽  
Homogeneous Linear

Abstract It is known that every solution to the second-order difference equation $x_{n}=x_{n-1}+x_{n-2}=0$ x n = x n − 1 + x n − 2 = 0 , $n\ge 2$ n ≥ 2 , can be written in the following form $x_{n}=x_{0}f_{n-1}+x_{1}f_{n}$ x n = x 0 f n − 1 + x 1 f n , where $f_{n}$ f n is the Fibonacci sequence. Here we find all the homogeneous linear difference equations with constant coefficients of any order whose general solution have a representation of a related form. We also present an interesting elementary procedure for finding a representation of general solution to any homogeneous linear difference equation with constant coefficients in terms of the coefficients of the equation, initial values, and an extension of the Fibonacci sequence. This is done for the case when all the roots of the characteristic polynomial associated with the equation are mutually different, and then it is shown that such obtained representation also holds in other cases. It is also shown that during application of the procedure the extension of the Fibonacci sequence appears naturally.

Optimal designs for collapsed homogeneous linear model

2021 ◽  
pp. 1-27
Author(s):  
Xuebo Sun ◽  
Yingnan Guan
Keyword(s):  
Linear Model ◽  
Optimal Designs ◽  
Homogeneous Linear

The product of non-homogeneous linear forms. II The minimum of a class of non-homogeneous linear forms

1954 ◽  
Vol 50 (3) ◽  
pp. 380-390 ◽  
Author(s):  
P. A. Samet
Keyword(s):  
Linear Forms ◽  
Cubic Fields ◽  
Homogeneous Linear

In this paper we determine the first minimum of a class of linear forms associated with certain cubic fields that depend on a parameter.

Homogeneous Linear Equations

2017 ◽  
pp. 79-104
Author(s):  
Kenneth Kuttler
Keyword(s):  
Linear Equations ◽  
Homogeneous Linear
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