Nonlinear Diophantine equation 11 x +13 y = z 2

Indonesian Operations Research Association - International Conference on Operations Research 2017

Sugandha, A.^1 ; Tripena, A.^1 ; Prabowo, A.^1 ; Sukono, F.^2

Mathematics Department, Faculty of Mathematics and Science, Universitas Jenderal Soedirman, Purwokerto, Indonesia^1

Mathematics Department, Faculty of Mathematics and Science, Universitas Padjajaran, Indonesia^2

关键词: congruency theory;    Diophantine equation;    Non linear;    Non negatives;    simulation;    Whole numbers;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/332/1/012004/pdf
DOI  :  10.1088/1757-899X/332/1/012004

来源: IOP

【 摘 要 】

This research aims to obtaining the solutions (if any) from the Non Linear Diophantine equation of 11x+ 13y= z2. There are 3 possibilities to obtain the solutions (if any) from the Non Linear Diophantine equation, namely single, multiple, and no solution. This research is conducted in two stages: (1) by utilizing simulation to obtain the solutions (if any) from the Non Linear Diophantine equation of 11x+ 13y= z2and (2) by utilizing congruency theory with its characteristics proven that the Non Linear Diophantine equation has no solution for non negative whole numbers (integers) of x, y, z.