Open AccessOn the Diophantine Equation n^x + 13^y = z^2 where n = 2 (mod 39) and n + 1 is not a Square Number
Author(s) -
gluk Viriyapong,
Chokchai Viriyapong
Publication year - 2021
Publication title -
wseas transactions on mathematics
Language(s) - English
Resource type - Journals
eISSN - 2224-2880
pISSN - 1109-2769
DOI - 10.37394/23206.2021.20.45
Subject(s) - diophantine equation , integer (computer science) , mathematics , mod , square (algebra) , square number , combinatorics , diophantine set , number theory , discrete mathematics , geometry , computer science , programming language
The purpose of the present article is to prove that the Diophantine equation n^x + 13^y = z^2 has exactly one solution (n, x, y, z) = (2, 3, 0, 3) where x, y and z are non-negative integers and n is a positive integer with n ≡ 2 (mod 39) and n + 1 is not a square number. In particular, (3, 0, 3) is a unique solution (x, y, z) in non-negative integers of the Diophantine equation 2^x + 13^y = z^2