On the Diophantine equation (p + 2)x ? p y = z 2 , where p is prime and p ? 5 (mod 24)

被引：0

作者：

Tadee, Suton ^{[1
]}

Laomalaw, Napalai ^{[1
]}

机构：

[1] Thepsatri Rajabhat Univ, Dept Math, Fac Sci & Technol, Lopburi 15000, Thailand

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE | 2023年 / 18卷 / 02期

关键词：

Diophantine equation; Mihailescu's Theorem;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we show that (0,0, 0) is the unique non-negative integer solution (x, y, z) for the Diophantine equation (p + 2)(x) - p(y) = z(2), where p is prime and p= 5 (mod 24).

引用

页码：149 / 152

页数：4

共 50 条

[1] On the Diophantine Equation 4(x) - p(y) = 3z(2) where p is a Prime
Tiongson Rabago, Julius Fergy
THAI JOURNAL OF MATHEMATICS, 2018, 16 (03): : 643 - 650
[2] DIOPHANTINE EQUATION P2X4+3PX2Y2+Y4=Z2, P AN ODD PRIME
SINHA, TN
JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS SECTION B-MATHEMATICAL SCIENCES, 1975, 79 (1-2): : 41 - 44
[3] EQUATION X2P+Y2P=Z2P
TERJANIAN, G
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1977, 285 (16): : 973 - 975
[4] On the Diophantine Equation 22nx - py = z2, where p is a prime
Orosram, Wachirarak
Unchai, Ariya
INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2022, 17 (01): : 447 - 451
[5] On the Diophantine equation (5pn2 -1)x + (p(p-5)n2 +1)y = (pn)z
Alahmadi, Adel
Luca, Florian
BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 2022, 65 (01): : 3 - 12
[6] On the diophantine equation x(2)-p(m)=+/-y(n)
Bugeaud, Y
ACTA ARITHMETICA, 1997, 80 (03) : 213 - 223
[7] THE EQUATION X2P + Y2P + Z2P = W2P
POWELL, BJ
FOSTER, LL
AMERICAN MATHEMATICAL MONTHLY, 1981, 88 (06): : 445 - 445
[8] The characterization of PSL(2, p) (p ≡ ±5 (mod 24))
Guan, Yunfei
Yan, Quanfu
Shen, Zhencai
COMMUNICATIONS IN ALGEBRA, 2024, 52 (07) : 2769 - 2773
[9] On the Diophantine Equations (p +a)x -py =z2 and px- (p +a)y =z2
Tadee, Suton
Wannaphan, Chantana
INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2024, 19 (02): : 459 - 465
[10] The Complete Set of Non-negative Integer Solutions for the Diophantine Equation (pq)2x+py = z2, where p, q, x, y, z are non-negative integers with p prime and p does not divide q
Pintoptang, Umarin
Tadee, Suton
INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2023, 18 (02): : 205 - 209

← 1 2 3 4 5 →