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Start Over Author "Akhtari, Shabnam" Journal journal fur die reine und angewandte mathematik
1 results on '"Akhtari, Shabnam"'

1. The Diophantine equation aX4 – bY2 = 1.

Author

Akhtari, Shabnam

Subjects
*DIOPHANTINE equations, *DIOPHANTINE analysis, *EQUATIONS, *ALGEBRA, *MATHEMATICS, *NUMBER theory
Abstract

As an application of the method of Thue-Siegel, we will resolve a conjecture of Walsh to the effect that the Diophantine equation aX4 – bY2 = 1, for fixed positive integers a and b, possesses at most two solutions in positive integers X and Y. Since there are infinitely many pairs ( a, b) for which two such solutions exist, this result is sharp. [ABSTRACT FROM AUTHOR]

Published
2009
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