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On a Diophantine Equation

โœ Scribed by Erdos, P.


Book ID
120099231
Publisher
Oxford University Press
Year
1951
Tongue
English
Weight
102 KB
Volume
s1-26
Category
Article
ISSN
0024-6107

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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).