On the Generalized Ramanujan–Nagell Equation x2+D=pz

✍ Scribed by Clemens Heuberger; Maohua Le

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 166 KB
• Volume: 78
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1999.2415

✦ Synopsis

Let p # [3, 23] and D # N such that p |3 D and (D, p){(2, 3). We prove in this paper that the diophantine equation

x, z # N has at most one solution (x, z). Moreover, we give an explicit upper bound for z.