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On the Diophantine equation

✍ Scribed by Florian Luca; Gökhan Soydan

Book ID
116673101
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
148 KB
Volume
132
Category
Article
ISSN
0022-314X

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On the diophantine equation
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✍ 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

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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).

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