Solutions to Non-Linear Diophantine Equation 2 ( 5) x y p p z 2 with p is Mersenne Prime
Agus Sugandha1, Agung Prabowo2, Agustini Tripena3
1Agus Sugandha, Department of Mathematics, Universitas Jenderal Soedirman, Indonesia.
2Agung Prabowo, Department of Mathematics, Universitas Jenderal Soedirman, Indonesia.
3Agustini Tripena, 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: 237-238 | Volume-8 Issue-2S7 July 2019 | Retrieval Number: B10600782S719/2019©BEIESP | DOI: 10.35940/ijrte.B1060.0782S719
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© 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) x y p p z with p is Mersenne prime. 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, which are using simulation to seek for solution (if any) to non-linear Diophantine equation 2 ( 5) x y p p z with p is Mersenne prime and using Catalan’s conjecture and characteristics of congruency theory. it is proven that the non-linear Diophantine equation has no solution for p 3.
Keywords: Non-linear Diophantine Equation, Solution, Catalan’s Conjecture.
Scope of the Article: Cryptography and Applied Mathematics