Open AccessOn the Diophantine Equation 3x + p5y = z2
Author(s) -
Kittipong Laipaporn,
Saeree Wananiyakul,
Prathomjit Khachorncharoenkul
Publication year - 2019
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.2019.6933
Subject(s) - diophantine equation , mathematics , legendre's equation , modulo , diophantine set , prime (order theory) , prime number , discrete mathematics , pure mathematics , algebra over a field , combinatorics
In this paper, we present new series of solutions of the Diophantine equation 3x + p5y = z2 where p is a prime number and x; y and z are nonnegative integers using elementary techniques. Moreover, the equation has no solution if p is equivalent to 5 or 7 modulo 24.