✦ LIBER ✦

On the diophantine equation

✍ Scribed by Pingzhi Yuan

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 168 KB
Volume: 112
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2004.12.002

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we prove the equation in the title has no positive integer solutions (x, y, n) with 2 | n and x = y apart from (x, y, n) = (5, 2, 5), (90, 2, 13).

📜 SIMILAR VOLUMES

On the diophantine equation

✍ Pingzhi Yuan; Yongzhong Hu 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 192 KB

Let D > 2 be a positive integer, and let p be an odd prime not dividing D. In this paper, using the deep result of Bilu, Hanrot and Voutier (i.e., the existence of primitive prime factors of Lucas and Lehmer sequences), by computing Jacobi's symbols and using elementary arguments, we prove that: if

On the diophantine equation y2 − D = 2k

✍ Nicholas Tzanakis 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 672 KB

On the diophantine equation x2 − Dy2 = n

On the diophantine equation x2 − Dy2 = nz2

✍ Edward L. Cohen 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 251 KB

On the diophantine equation x2 + D = 4pn

✍ Le Maohua 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 376 KB

On the diophantine equation x2−D = 4pn

✍ Le Maohua 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 518 KB

On the diophantine equation x2+D=4yq

✍ W. Ljunggren 📂 Article 📅 1971 🏛 Springer Vienna 🌐 English ⚖ 334 KB