Open AccessNon-negative Solutions of the Nonlinear Diophantine Equation (8^n)^x + p^y=z^2 for Some Prime Number p
Author(s) -
Boorapa Singha
Publication year - 2021
Publication title -
walailak journal of science and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.146
H-Index - 15
eISSN - 2228-835X
pISSN - 1686-3933
DOI - 10.48048/wjst.2021.11719
Subject(s) - integer (computer science) , diophantine equation , modulo , prime (order theory) , mathematics , generalization , nonlinear system , prime number , discrete mathematics , combinatorics , physics , mathematical analysis , computer science , quantum mechanics , programming language
In this paper, we explain all non-negative integer solutions for the nonlinear Diophantine equation of type 8x + py = z2 when p is an arbitrary odd prime number and incongruent with 1 modulo 8. Then, we apply the result to describe all non-negative integer solutions for the equation (8n)x + py = z2 when n ≥ 2. The results presented in this paper generalize and extend many results announced by other authors.HIGHLIGHTSStudying a new series of the equation 8x + py = z2 when p is prime which is not congruent to 1 modulo 8Describing all non-negative integer solutions of the equation (8n)x + py = z2 which is a generalization of the equation 8x + py = z2The equation 8x + py = z2 has at most 3 non-negative integer solutions when p is congruent to 1 modulo 8 and p ≠ 17