Non-negative Integer Solutions of Some Diophantine Equations
Somchit Chotchaisthit* Author for corresponding; e-mail address: somchit@kku.ac.th
Volume: Vol.44 No.3 (July 2017)
Research Article
DOI:
Received: 8 September 2014, Revised: -, Accepted: 6 April 2015, Published: -
Citation: Chotchaisthit S., Non-negative Integer Solutions of Some Diophantine Equations, Chiang Mai Journal of Science, 2017; 44(3): 1163-1171.
Abstract
In this paper, it is shown that for any non-negative integers m and n, all non-negative integer solutions of the Diophantine equation 43n2x + 43y = z2m are the from (3, n, 3(43)) if m = 1 and n is even, and it has no solution in the case m 1 or n is odd. It is also shown that all non-negative integer solutions of the Diophantine equation 2x + 2n43y = z2m are the following forms: