WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 20, 2021
On the Diophantine Equation nx + 13y = z2 where n = 2 (mod 39) and n + 1 is not a Square Number
Authors: ,
Abstract: The purpose of the present article is to prove that the Diophantine equation nx + 13y = z2 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 2x + 13y = z2.