Solutions to Non-Linear Diophantine Equation 2 (5 1) (5 ) k x k y z with k is Positive Even Integer
Agustini Tripena1, Agus Sugandha2, Agung Prabowo3
1Agustini Tripena, Department of Civil Engineering, Politeknik Negeri Ambon, Indonesia.
2Agus Sugandha, Department of Mathematics, Universitas Jenderal Soedirman, Indonesia.
3Agung Prabowo, Department of Mathematics, Universitas Jenderal Soedirman, Indonesia.
Manuscript received on 03 August 2019 | Revised Manuscript received on 26 August 2019 | Manuscript Published on 05 September 2019 | PP: 239-242 | Volume-8 Issue-2S7 July 2019 | Retrieval Number: B10610782S719/2019©BEIESP | DOI: 10.35940/ijrte.B1061.0782S719
Open Access | Editorial and Publishing Policies | Cite | Mendeley | Indexing and Abstracting
© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: This research seeks for a solution (if any) to non-linear Diophantine equation 2 (5 1) (5 ) k x k y z . There are 3 possibilities of solution to the non-linear Diophantine equation, which are single solution, many solutions, or no solution. The research methodology is conducted in two stages has t, which are using simulation to seek for a solution (if any) to non-linear Diophantine equation 2 (5 1) (5 ) k x k y z and using Catalan’s conjecture and characteristics of congruence theory. It is proven that the non-linear Diophantine equation has single solution 2 ( , , ) (1,0,5 ) k x y z for non-negative integer x, y,z and positive even of equal to or higher than.
Keywords: Non-linear Diophantine Equation, Solution, Catalan’s Conjecture.
Scope of the Article: Cryptography and Applied Mathematics