The Solution for the Non linear Diophantine Equation (7k -1)x +(7k)y = z2 with k as the positive even whole number. (July 2019)

• Record Type: Journal Article
• Authors: Rahmawati, R; Sugandha, A; Tripena, A; Prabowo, A
• Is Part Of: Journal of physics. Volume 1179(2019)
• Publication Date: 2019-07
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1179/1/012001
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: This research may provide the solutions (if any) from the Non-linear Diophantine equation (7 k — 1) x + (7 k ) y = Z 2 .There are 3 possibilities to determine the solutions from the Non-linear Diophantine equation: single solution, multiple solutions, and no solution. The research method is conducted in two stages: first, using a simulation to determine the solutions (if any) from the Non-linear Diophantine equation (7 k — 1) x + (7 k ) y = z 2 ; second, using Catalan conjecture and characteristics of congruency theory, which is proven that the Non- k linear Diophantine equation has a single solution ( x, y, z ) = ( 1, 0, 7 k 2 ) for x, y, z as non-negative whole numbers and k as the positive even whole number.