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Discussions: On a Diophantine Equation

✍ Scribed by H. C. Bradley

Book ID: 123765585
Publisher: Mathematical Association of America
Year: 1921
Tongue: English
Weight: 122 KB
Volume: 28
Category: Article
ISSN: 0002-9890
DOI: 10.2307/2971782

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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).