An algorithm for solving systems of linear diophantine equations in naturals

1997 ◽  
pp. 73-84 ◽  
Author(s):  
Ana Paula Tomás ◽  
Miguel Filgueiras
Keyword(s):  
Diophantine Equations ◽  
Linear Diophantine Equations

Coordination sequences and layer-by-layer growth of periodic structures

2019 ◽  
Vol 234 (5) ◽  
pp. 291-299
Author(s):  
Anton Shutov ◽  
Andrey Maleev
Keyword(s):  
Generating Functions ◽  
Diophantine Equations ◽  
Periodic Structures ◽  
Layer Growth ◽  
Layer By Layer ◽  
Explicit Formulas ◽  
New Approach ◽  
Coordination Numbers ◽  
Linear Diophantine Equations ◽  
Recurrent Relations

Abstract A new approach to the problem of coordination sequences of periodic structures is proposed. It is based on the concept of layer-by-layer growth and on the study of geodesics in periodic graphs. We represent coordination numbers as sums of so called sector coordination numbers arising from the growth polygon of the graph. In each sector we obtain a canonical form of the geodesic chains and reduce the calculation of the sector coordination numbers to solution of the linear Diophantine equations. The approach is illustrated by the example of the 2-homogeneous kra graph. We obtain three alternative descriptions of the coordination sequences: explicit formulas, generating functions and recurrent relations.

scholarly journals On the Non-Linear Diophantine Equations 31x + 41y = z2 and 61x + 71y = z2

2018 ◽  
Vol 18 (2) ◽  
pp. 185-188
Author(s):  
Satish Kumar ◽  
◽  
Deepak Gupta ◽  
Hari Kishan
Keyword(s):  
Diophantine Equations ◽  
Linear Diophantine Equations ◽  
Non Linear

Few Non-Linear Diophantine Equations

2021 ◽  
pp. 295-306
Author(s):  
Satyabrota Kundu ◽  
Sypriyo Mazumder
Keyword(s):  
Diophantine Equations ◽  
Linear Diophantine Equations ◽  
Non Linear
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